Than compares things, but then is all about time. They sound similar and were even spelled the same until the 1700s. Not anymore! Vive la difference!
Than shows comparison and has words on either side. A giraffe is bigger than a weasel. A pickle tastes better than a shoe. Than shows up in familiar sayings:
It's better to give than to receive.
Actions speak louder than words.
His bark is worse than his bite.
Problems arise when a pronoun follows than. Is it "She is taller than I"? Or "She is taller than me"? If you said "taller than I," you are correct! Because of the understood verb — "She is taller than I (am)" — you use I not me. (If that sounds a little stuffy, don't worry. Over the years it's become okay to save "taller than I" for formal writing and use "taller than me" informally.)
Okay, then, let's talk about then. Then doesn't bother comparing anything, it just moves things along. Then can be used as in "next," or "at a particular time," or "in that case." It often comes after an "if" as in "If we write about cats, then we must write about dogs." And then there were examples:
She got up at 4 a.m. to practice, then went to school, then got back in the pool to practice some more. (Washington Post)
Moun was treated by prison medical staff, then taken to a hospital, where he was pronounced dead. (Los Angeles Times)
Getting these imports at a cheaper price, then, is good news. (US News)
There you have it. Than is higher in the alphabet than the word then. When making comparisons, than gets an A because it's more competitive. It's even first in the alphabet! Then has an "e" because it's n-e-xt.