You have two basic options for controlling 3 Rail O Gauge:
1.) Conventional -- Everything back in the day (1900-1994 roughly) used this method for control. There's a throttle lever or knob on your transformer that controls speed (and usually direction as well) by varying the voltage (0-18v AC or so) applied to the track. In the late 90's some very sophisticated ways of controlling more advanced features in conventional mode were developed (like MTH's original Protosound, or QSI), but all of those use the standard whistle and/or bell buttons, and/or movement of the throttle handle, found on the standard transformer to activate them. They are not command systems.
2.) Command -- Optional since about 1994. Full voltage (18v AC or so normally) is applied to the track but the locomotive doesn't immediately fly around the track as long as everything is connected correctly. Instead a separate command signal is sent to the loco to tell it to move, and whistle, and chatter radio calls, and turn lights on and off, and about 10,000 other fancy things too. You use a wireless (usually) handheld controller to send the commands.
TMCC and Legacy are Lionel's form of command control. The command signal is sent by radio from the control base (CAB-1 for TMCC, CAB-2 or CAB-1L for Legacy and TMCC) to the locomotive.
DCS (Protosound 2 or 3) is MTH's form of command control. The command signal is sent by from the control base (TIU, DCS Explorer, etc.) by impressing it upon (modulating) the AC voltage used to power the track.
DCC is the 2-Rail (largely) form of command control, is used largely with DC power as a result, and is thus commonly also used in HO, N, and G scales. The command signal also modulates the power to the track. It is quite rare in 3 Rail O Gauge.
For the most part the first two, TMCC/Legacy and DCS, do not interfere with each other. This means that you can usually use them at the same time on the same track, but to do so each normally needs its own separate controller. You may also need a special filter (a 22 uH choke in series with one of the the power leads on offending equipment) for DCS to work if some Lionel products are on, or connected to, the same track.
Lionel products need only one CAB-1/CAB-1L/CAB-2 per layout to operate, and MTH need at least one TIU/DCS Explorer, etc. There is one exception: DCS controllers will control Lionel products in TMCC if you also add a Lionel command base connected to your TIU command base setup. Same for Legacy with a slightly different, but similar, set of connections.
For Lionel CAB-2 equipment supercedes CAB-1, that is, it does everything that CAB-1 does, i.e. TMCC, and more. The 'more' is Legacy. CAB-1L is a lower cost CAB-2, having reduced Legacy features but all TMCC ones.
Important (finally): All command locos are backwards compatible, that is they will also operate in 'conventional' mode, usually with reduced features as a concession, as long as they do not receive the "carrier" for their command signal. All command bases, if present, or even if nearby for Lionel stuff, must be powered off to ensure that the carrier is not sent, allowing you to run the command locos in conventional mode.
Hope this helps.