Split tones are just as described above. Unless it is DCS, which is really not a tone, it's a digital code. Those codes can run normal polarity (N) or, reverse polarity (R) on either transmit or, receive. We have a repeater in Phoenix that runs split DCS, (programing = CROSS, 071N, 225N, CROSS -> CROSS) as well as travel tone. The DCS (or DTCS as it may be referred to when programing) is used for normal everyday traffic and, as a means of keeping the repeater private for members only. The travel tone is programed into a separate channel (same repeater frequencies) in the radio and used for weekly nets, another set of tones is for tactical (emergency services), and so on. This way, members that don't want to listen to the net can stay on their "home" channel with the DCS, and not hear the net traffic.
Radios that are capable of using distinct, different, DCS codes are not that easy to find. Most times you have to ask the manufacturer the specific question. That said, most commercial radios (part 90), should be able to handle it. The Baofeng UV82C is one such handheld.
Hope this helps!