Twinax is an interconnect by IBM, it encompasses everything from cable to the communication protocol.
RJ45 is a plug and nothing more. You can attach it to absolutely anything.. 110V mains - no problem, cable TV - go ahead, feel free to use it as a door to your ant farm Whether this kind of connection is "standard" or of any use, is another matter.
There are controllers that let you tunnel twinax across TCP/IP. I don't think you can feed twinax directly through CAT5 or any other cables - the thing seems to want termination and such and a non-twinax cable will probably break it.