What is the difference between take tea and drink tea?
In American English, we do not "take" tea. We have tea, or drink tea. Drink is the act of swallowing a liquid.
"Having tea" means an occasion of an entire tea ceremony, or tea party, or social gathering where tea is served. One part of that (not the most important part) is drinking the tea. If I invite my friend,
(Perspective from BrE speaker.) "take tea" feels like something done by genteel ladies in an old book; it is not an expression that is much used nowadays, and may sound strange if dropped into a modern conversation.