Definition: A polite expression used when acknowledging a gift, service, or compliment, or accepting or refusing an offer; expression of gratitude or appreciation.
This basic ASL word THANK-YOU is inflectable to reflect the verb "THANK" in agreement with the subject-object order. E.g. THANK-HIM/HER.
One-handed and two-handed versions with a number of movements convey different meanings in contexts.
If you sign THANK-YOU with both hands (and sometimes with the movement than once), it can express as thank you very much." If using both hands plus two movements or more, it can express as "many thanks" or THANKFUL, when one feel much appreciation. It's not a black-and-white rule, it depends on contexts and intonation.
First 100 words.
As you feel more comfortable with the first few hundreds of ASL signs, progress further with your vocabulary and learn signing more.