.mov, .ts, .mts, .m2ts are containers with specifications.
Ignore the post about .mov being highly compressed. Although they *can* be, they are not always going to be - and won't be if the container has ProRES video in it (a simple example, a project I have that is 720p, ProRES 422 (obviously a .mov container) @ 1hr6min is ~72Gig - this is normal.
.mov files can contain a variety of different codecs
ProRes is a codec. ProRES video has very little compression to it and is extremely easy to edit. The ProRES codec can be stored within a .mov container. There are 2 major versions of ProRES, the original ProRES - also known as ProRES 422 and the new ProRES that came with Final Cut Studio 3 - also known as ProRES 444.
Quicktime Video (as used in export to quicktime video) is really just another way to refer to .mov files.
.mts (MPEG Transport Stream) files are containers that hold video, audio and potentially data. It is just a container that has specifications on the type of codecs and how the audio, video, etc. should be stored within the container.
As you're editing in Final Cut Pro (per your other thread on the MTS/M2TS topic that we had discussed), you will not transcode the mts yourself, you'll do a log and transfer of the footage which will handle converting the very hard to edit highly compressed footage to the much more edit friendly ProRES codec within a .mov container.