I'm not familiar with any of the units that you have listed, the first two are toners also known as tracers and the last two appear to be combined toners with an incorporated single end to end cable map feature, probably suitable for smaller applications in regards to mapping, should be fine for tracing as they are all pretty much the same for that task, we use dedicated testers for tracing/ toning and completely separate testers for mapping, cable and signal integrity.
For Lan, security and other multi pair cables our basic mapping tester sets have multiple numbered termination adaptors so we can run around and connect them to the ends of the cables and then go back to the comms room and place many identification labels in one go, for most of these types of testers it's a good idea to make up some short RJ-45 to quick connect cables so as to perform multi pair testing on unterminated cabling such as security and the like.
Generally for mapping you would already have the cable plugs and sockets fitted and finished so you can readily patch in to the onboard RJ-45 testers socket, you would trace and label your cables first then terminate plugs and sockets, then map the pairs checking for shorts, opens and crossed pairs. Some of the better cable testers on a budget that I have seen have multiple termination adaptors available and even incorporate a very basic cable length feature, these are handy.
For more indepth testing and diagnostics we use other equipment but for your average joe in a residential situation any of the ones listed above should get you out of trouble.
If I had to choose from the four that you listed it would be the first one (MS6812) as a toner/ tracer only because it has adjustable receive sensitivity and as a toner/ tracer/ mapper it would be the forth one (FY868) for the same reason and it has a BNC on the transmitter for coax.
Muttley