There are a few concertina looking instruments that have chord buttons. They usually seem to be eight bass, two row diatonic accordians or the Italian one-and-a-half row forced into a 6 sided concerina shape. There is also a version of a Bandoneon called, IIRC, a Bandonika which, again is a diatonic accordian in concertina clothing.

My personal preference (and seems totally logical to me) is that if one button produces a chord it's an accordian, if it doesn't it's a concertina (except that free bass piano accordians would be reclassified as a concertina ).