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Any bike that can fold is a "folding bike"

A bike with 20" (or smaller) wheels, but does not fold or break down, is a "mini-bike."

A bike with any size wheels that can be broken down for travel (e.g. Moulton 20", Ritchey 700c Breakaway, Air Friday), but does not have a quick fold, is usually called a "separatable."

Of course any bike that folds is a "folding bike", but since most folding bikes have 16 or 20 inch wheels, I like to call the ones with bigger wheels (26" or 700c) "full sized folding bikes" and the ones with smaller wheels (12", 8", or 6") "mini folding bikes".

I don't like the term 'mini-bike'. It sounds like a toy. Bikes with 16" or 20" wheels can be just as capable as any other.

I thought the non-folding 20" bikes were called mini-velos.