The name State of Mind in Chinese / Japanese...

初心 is often translated in Japanese as “beginner's mind” or “beginner's spirit.”

In Chinese, the dictionary definition is “one's original intention.”

The first character means first, initial, primary, junior, beginning, or basic.

The second character means heart, mind, soul, or essence.

初心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: The state of shoshin is that of a beginners mind. It is a state of awareness that always remains fully conscious, aware, and prepared to see things for the first time. The attitude of shoshin is essential to continued learning.

無事 is a Zen Buddhist term meaning no problem and no trouble.

無事 is the Zen state of perfect freedom from troubles and leaving secular affairs behind.

Sometimes this is used to describe the state of satori and complete tranquility of mind.

Written as 無事に with an extra Hiragana at the end, this becomes an adverb to describe something in the condition of safety, peace, quietness, and without troubles.

無事 (Buji) can also be a given name in Japan.

This has more meaning in the Japanese Zen Buddhist community than in China or Korea, where it can mean “be free” or “nothing to do or worry about.”

失意泰然 is a very old Japanese proverb that suggests “keeping calm and collected at times of disappointment,” or “maintaining a serene state of mind when faced with adversity.”

It's hard to relate individual character meanings to the overall meaning unless you also understand Japanese grammar. The word order is very different than English. That being said, here's the character meaning breakdown:
失 To miss, lose or fail.
意 Feelings, thoughts, meaning.
泰 Safe, peaceful.
然 Like that, in that way, however, although.

Using these definitions in English, we might say, “Although you may fail or lose, have a feeling of peace and calm.”

不動心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet.

Under that context, places such as the Budo Dojo define it this way: An unshakable mind and an immovable spirit is the state of fudoshin. It is courage and stability displayed both mentally and physically. Rather than indicating rigidity and inflexibility, fudoshin describes a condition that is not easily upset by internal thoughts or external forces. It is capable of receiving a strong attack while retaining composure and balance. It receives and yields lightly, grounds to the earth, and reflects aggression back to the source.

Other translations of this title include imperturbability, steadfastness, keeping a cool head in an emergency, or keeping one's calm (during a fight).

The first two Kanji alone mean immobility, firmness, fixed, steadfastness, motionless, and idle.

The last Kanji means heart, mind, soul, or essence.

Together, these three Kanji create a title defined as “immovable mind” within the context of Japanese martial arts. However, in Chinese, it would mean “motionless heart,” and in Korean Hanja, “wafting heart” or “floating heart.”

First off, 殘心 should only be used in the context of Japanese martial arts. In Chinese, it's a rather sad title (like a broken heart). In Chinese, the first character alone means destroyed, spoiled, ruined, injured, cruel, oppressive, savage, incomplete, or disabled. However, in Japanese, it's remainder, leftover, balance, or lingering.
The second character means heart, mind, soul, or essence in both languages.

殘心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: The spirit of zanshin is the state of the remaining or lingering spirit. It is often described as a sustained and heightened state of awareness and mental follow-through. However, true zanshin is a state of focus or concentration before, during, and after the execution of a technique, where a link or connection between uke and nage is preserved. Zanshin is the state of mind that allows us to stay spiritually connected, not only to a single attacker but to multiple attackers and even an entire context; a space, a time, an event.

In modern Japan (and Simplified Chinese), they use a different version of the first character, as seen to the right. Click on this character to the right instead of the button above if you want this modern Japanese version of lingering mind / zanshin.

In Japanese, 無心 means innocent or without knowledge of good and evil. It literally means “without mind.”

無心 is one of the five spirits of the warrior (budo) and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: “No mind, a mind without ego. A mind like a mirror which reflects and dos not judge.” The original term was “mushin no shin,” meaning “mind of no mind.” It is a state of mind without fear, anger, or anxiety. Mushin is often described by the phrase “Mizu no Kokoro,” which means “mind like water.” The phrase is a metaphor describing the pond that clearly reflects its surroundings when calm but whose images are obscured once a pebble is dropped into its waters.

This has a good meaning in conjunction with Chan / Zen Buddhism in Japan. However, out of that context, it means mindlessness or absent-mindedness. To non-Buddhists in China, this is associated with doing something without thinking.
In Korean, this usually means indifference.

Use caution and know your audience before ordering this selection.

More info: Wikipedia: Mushin

安心 can be defined as relief, peace of mind, feeling at ease, to be relieved, to set one's mind at rest, and easiness.

安心 is a nice word that encompasses great meanings within just two characters. Some of the other meanings include pacifying, settling the mind, and peace of mind. It's also the idea of feeling a sense of security, safety, and confidence in your state of well-being.

This can be used by everyone, but some consider it to be a Buddhist concept (You'll find it in your Zen dictionary).

Note: Can be romanized as Anshin or Anjin in Japanese.

心澄淨 is the Buddhist concept of the pure and calm mind. It is believed that once you achieve a meditative state of pure focused thought, the mind becomes clear and calm. Although, others will say this means that achieving a calm mind will allow you to reach pure thought.

From Sanskrit, this is known as citta-prasāda. The concept of citta-prasāda is sometimes defined as “clear heart-mind,” or “the single and definitive aspiration.”

三昧 is the Chinese, Japanese Kanji, and old Korean Hanja way to write Samādhi.

Samadhi is the state of intense concentration achieved through meditation.

Some will define Samādhi as putting together, composing the mind, intent contemplation, perfect absorption, or union of the meditator with the object of meditation.

定 is the single-character way to express the idea of Samadhi in Chinese and Japanese.

A single-character title like this is open to a lot of interpretation. So 定 can mean to set, to fix, to determine, to decide, to order, certainly, truly, settle, or compose the mind.

In the Buddhist context, this means “Perfect absorption of thought into the one object of meditation,” “The mind fixed in one direction,” “Internal state of imperturbability or tranquility,” or “Exempt from all external sensations.”

入靜 is used in Taoism and Qi Gong to describe the state you can reach while sitting quietly in meditation. It contains the idea of achieving a highly-tranquil and peaceful state. Some may describe this state as “sleeping while still awake.”

If you have a relaxation or meditation room, this is the calming wall scroll that you would want hanging in that room.

Hishiryō (非思量) literally means not-thinking.

Hishiryo can be described as a state of mind beyond thinking and non-thinking during the practice of Zazen.

Shiryō (思量) means “thinking,” and hi (非) is a prefix for negation and opposition.

Therefore, hishiryo amounts to “unthink” or “not the matter of thinking.” The word hishiryo appears in Dogen Zenji’s Fukanzazengi, Shobogenzo Zazengi, Shobogenzo Zazenshin, and Keizan Zenji’s Zazen Yojinki. It is one of the most important words used to describe zazen. Hishiryo in these writings comes from a dialogue between Yakusan Igen (745-828) and an unnamed monk, which is described in Keitoku, Dentoroku, and other Zen texts.

The above is an abridged except from School of Shodo: Hishiryo
I suggest you visit that page for a full explanation.