It is unnesessary to ask to read for more details in your subject headings. That's understood.
Basically, for our purposes, firewire, also called IEEE1394, is the protocol of how signals get in and out of the computer.
Vegas uses a firewire connection which will either be built into your motherboard (and you computer will then have a firewire connector somewhere on it) or an add-on card (these cost about $35).
As long as it is OCHI compliant (almost all are), you are good to go. No other cards are needed.
I belive Apple start using Firewire (called I-Link for them, isn't it?) before PC's started using them (isn't that almost always the case? :) ). There's a couple versions of Firewire out/comming out (a,b?). Each version has less restriction then the previous (max transfer rate, more devices connected to a port at once).
The Matrox RT cards are compatible with Vegas as long as you don't use them for anything else then a firewire card (ie a $500-1000 firewire card). The RT aspect only includes Premiere. You do get a copy of Premiere with these cards though (kinda like the fine print in a loan :) ).
If you want a firewire card with analog support, get the Canapus ACDVio card. it includes a copy of Vegas too. Great deal for around $500!