The largest difference is the way the collet is closed or squeezed. Take the DA style for instance, (DA is for double angle) it uses two fairly small angled/tapered ares to squeese the collet against the tool being held. TG collets use one long taper that runs almost the entire length of the collet. ER collets are sort of a mix of a long and a short tapered area. All the collets you mentioned use a nut in front of the collet to close it except for the C style. C collets (similar to R type) are mostly used in machine spindles and attachments and they are typicaly drawn tight the back of the collet. Think of an R8 in a bridge port spindle or the C type used in many tool grinding fixtures.