The only similarity is that they sound similar. Once you know what they mean you'll never confuse them! "Than" is a preposition used for comparison e.g. "The dog was bigger than the cat". "Then" is an adverb which means "after that" e.g. "We went to the beach, then we went to the movies". "Then" has a few other, less common meanings, none of which are similar to "than".

then is about time. I got wet then I went home. than is comparison. warmth is much better than the cold.