JP,
Although I'm not sure that there is any publication or standard anywhere that defines the terms, a collet chuck usually is a gadget that attaches to the spindle. In all Atlas cases it would screw onto the spindle nose threads.
A collet adapter, also called a collet closer, would stick into the spindle, in this case 2MT for the Atlas Mill and 6" lathes and 3MT for the larger Atlas lathes (9", 10" and 12"). An end mill or cutter holder also usually sticks into whatever taper the machine has in the spindle bore. Using these definitions, the collet closer for traditional pull-type collets like 3AT and 5C costs very little table space. But neither will fit on an Atlsa 6" or mill. 2MT collets will. The collet adaptor (on a 2MT arbor) and the collet chuck for ER collets have a compression nut on the front which will take up something like an inch or more of table space. I don't think that anyone makes a collet chuck for a 5C collet that will fit the mill or 6". I have one for my 3996 and it sticks out about as far as my Pratt Bernard 3-jaw and is about 4" in diameter. So much too large to make to fit the mill or 6".
Sorry, but I do not have any of the ones that you might be interested in to take a photo of.
Robert D.