This information is provided by Accordion Lab http://acclab.com

What is a tone chamber?

A tone chamber, or Cassotto accordion has one or two reed sets, usually the L and an M set of reeds, installed vertically to the regular position. The tone chamber makes it possible for the sound produced by the reeds in the chamber to go through a different and longer path than the normally installed reeds, thus produce a deeper and mellow sound.  If there are two sets of reeds in the chamber, it is called a double tone chamber. 

      Treble reeds in tone chamber and regular position       

Most polka players do not use accordions with tone chambers.  They're more likely to be found in classical, Italian or jazz music. Some jazz musicians have all reeds chambered, additionally some only use bassoon and clarinet reeds.

Because a tone chamber accordion requires two separate treble reed valves for the regular reeds and for the reeds in the tone chamber respectively, it is structurally more complex, and more difficult to adjust and repair/service.  Some special accordion also has a tone chamber on the bass side.

What is the difference between the mute registers (aka Tone Modulator) and a tone chamber?

 They do two different things. The mute consist of two registers one turns it on and the other turns it off. Their effect is to change the sound by baffling off the sound by using something in or under the grill to cover the grill openings and making the sound softer. The usual mute is a slide that blocks the sound. Some types open or close large pads over holes on the font of the grill. Another type on some Hohner accordions rolls up like a window shade when open beneath the front grill.

 Tone modulators made of wood or metal hood that can be switched open (mute-off) or close (mute-on)