Synonyms are words with similar meanings, although the exact shade of meaning may be different. This post, however, deals with pairs of words that are not synonyms but pairs in which one member is sometimes, and erroneously, mistaken for the other.
In communicating what you mean, synonyms do not pose as serious a problem as confusables do. Nearly and Almost, for example, are practically interchangeable. But writing alternate when you mean alternative can jeopardize the clarity of what you are trying to convey.
The difference between alternate and alternative is equally clear cut-at least in British English: alternate implies two possibilities only one of which can occur at a given time; a bar code, for example, consists of alternating strips of black and white. If an event is described as occurring on alternate days and if it occurs, say, on Monday, it cannot occur on the Tuesday that follows. Alternate thus suggests taking turns: first one thing, then the other, and then the first thing again.
Alternative suggests options or choices: the sun and the wind are alternative sources of energy or an e-mail message is a faster alternative to "snail mail" (i.e., a message sent through the post office).