Formal expression of thankfulness, often used in written or official contexts.
I express my deep gratitude for your support.
Formal expression of apology; less common than 謝罪 in everyday speech, but used in official statements.
He expressed his apology for the mishandling.
The company expressed its gratitude to the customers who had supported it.
The company issued a formal statement of apology regarding the accident.
He conveyed his gratitude in a letter.
I accept this award with heartfelt gratitude.
謝罪 is the standard, widely used word for apologizing, while 謝意 in its apology sense is more formal and mainly appears in official statements.
謝辞 refers to the actual words or speech of thanks delivered on a formal occasion, whereas 謝意 refers to the abstract feeling or intent of gratitude itself.
Compound of 謝 (しゃ, 'apology' or 'thanks') and 意 (い, 'mind' or 'intention'), literally meaning 'feeling of apology/gratitude'. The dual meaning reflects the kanji 謝, which can express both apology and thanks.