Traditionally, a muffler has the exhaust exiting the inlet pipe through many small holes into the muffler body, then again through small holes into the outlet pipe. Multi chambered is an apt description.
A resonator is typically a straight through design, with a single perforated tube from inlet to outlet.
Now let me add that many manufacturers use both names interchangebly. The stock resonator on a 1st gen 3.5 is multi chambered, the ones on a 300 Special are straight through.
It's a bit of a crap shoot to get the sound/performance from a system without being able to test it first.
One of several experiences I've had with exhaust mods was a surprise. I removed the stock (read "restrictive") multi chamber muffler from my Kawasaki 4 stroke dirt bike, (KLX300), replaced it with a straight through model packed with fiberglass and have a much quieter yet high flow system.