Some "converters" are just simple-minded voltage converters (24VDC->12VDC) that lack the technology to *properly* monitor and charge a battery.
Most if not all "chargers", in addition to possibly converting voltages up or down, know how to monitor a battery's charge level and apply the appropriate bulk, absorb, float and maintenance charges.
It does seem many 120VAC->12VDC products are just called "converters" even though they have battery charging smarts too. And in the case of my Progressive Dynamics Inc. "converter with charge wizard", it can safely power things WITHOUT a battery.
The upshot, the terminology is not 100% standard, and I'd say you need to make sure the specs call out battery charging if that's one of the things you want.
--tg