感謝 and 感激: gratitude's target and what moves someone
Compare gratitude for help with being moved by a letter or performance, distinguishing gratitude put into a letter from a reaction to receiving one.
Gratitude directed toward helpers
感謝 (かんしゃ) means gratitude or thanks. “手伝ってくれた皆に心から感謝します。” sincerely thanks everyone who helped. The gratitude is directed toward those helpers.
“短い手紙に感謝の気持ちを込めた。” describes expressing gratitude in a short letter. It states putting that feeling into the letter without reporting its eventual delivery.
Being moved by a letter or performance
感激 (かんげき) describes being deeply moved. “思いがけない手紙を受け取り、深く感激した。” reports receiving an unexpected letter and being deeply moved. Its sender and specific contents are not supplied.
In “観客は心のこもった演奏に感激して拍手した。”, the audience applauded, moved by the heartfelt performance. The performance prompted the reaction, and applause is also stated.
Expressing a feeling and experiencing a reaction
The gratitude examples present helpers and an act of putting gratitude into a letter; the 感激 examples present reactions after receiving a letter or hearing a performance. Do not link the two letter examples into one exchange of the same letter.
Gratitude and being moved can coexist. However, being deeply moved alone does not establish receiving a particular person's help or performing an act of thanking them.
What actions do 感謝 in the short-letter example and 感激 in the unexpected-letter example describe?
Show the answer and why
The first describes expressing gratitude in a letter; the second describes receiving an unexpected letter and being deeply moved. The sentences do not state that they concern an exchange of the same letter.