Yes, they are similar.
But ‘appreciate’ is the verb and ‘thankful’ is the adjective.
You can say, ‘I appreciate your gift’, ‘I am thankful for your gift’, ‘I thank you for your gift’, but you cannot say, ‘I thankful your gift’,
‘Appreciate’ in the adjective form is ‘appreciative’, so you can say, ‘I am appreciative of your gift’.
I hope this is helpful. Good luck!
Jason