Most boards that we would be using (aka "prosumer" or "unbalanced" -10dB consoles) generally have some or all of the following I/O
Ins:
Mic In (XLR)
Line In (rca or phone)
Tape in or "Tape return" (rca or phone)
Aux return
Outs:
Direct out
Aux send
monitor out
Buss (line) out
Again, oversimplification, and will ignore the aux, monitor, etc. I am not familiar with your board, so I'll stick to the basic setup. (Also, there is often more than one way to get a signal to .e.g. your monitors, your headphones, etc, depending on your setup)
I started out with a small 6x2 (meaning 6 inputs 2 "buss" outputs) and a 4 track deck. From there I moved up to a Teac 5 (8x4) and a Tascam 38, then a M-520 (20x8) and a MSR-16. But the gozintas and gozoutas, generally stay the same conceptually.
The Teac 5/Tascam 38 (although the 5 board is really better suited to 4 track not 8 track) is probably easiest to envision and explain. I also have a four track 22-4, so let's use that as the example. A "standard" routing would be
Teac 5 buss outs -----> line ins Teac 22-4 (1-4)
Teac 22-4 line outs -----> Teac 5 Tape return (1-4)
The Teac 5 has one Aux ("Echo") so the Aux out ("Echo out") would be connected to a reverb device and the Echo return from that device. The "Cue out" would be sent to e.g. a headphone amp (I have a Behringer that allows four sets of headphones)
(****note that Aux usually is an effects send/return, so Aux send, effects send etc, are the same it happens to be called Echo on the Teac 5, and aux out refers to something else. -- inconsistent I know)
There is a switch at the top of the channel strip which is mic-tape-line. So if I'm recording, it will generally be mic or line, and if I'm mixing it will be 'Flipped" to tape.
There are more routing permutations, even on the Teac 5, but this hopefully isn't too muddled an explanation.
Normal:
I have a couple of 32 point patchbays (16 on top/16 on bottom) that are 'normalled.' (I don't remember top or bottom) at the moment, I'm not at them) so e.g. my board (M-520) is an 8 buss board. I generally use the buss outs rather than direct outs, although there are different schools of thought on that. The M-520 has two sets of buss outs (it's still 1-8, just two sets of 1-8) so unless I use the direct outs (which would require me to run extra cables) I can only record 8 tracks at once. Let's assume I'm OK with that. So, the buss outs go to the bottom of back of the patch bay. It is normalled, meaning that there is a connection between the bottom row of rca jacks and the top row of rca jacks on the back of the panel. So then I connect the top row to the ins of the MSR-16. But, if I want to use my Tascam 38, or Fostex A-8, I have the ins of those coming to yet another patch bay. I can "break the normal" by connecting an rca cable to the top row of the patch bay with the buss outs to the line in on the A-8, 38, what have you.
ADAT is a type of digital interface, 8 channels over an optical cable. The A I think stands for Alesis, but it's become something of a generic standard. TDIF is a Tascam interface, similarly AFAIK carries 8 channels of digital information.
I would guess you could find an PC interface card with TDIF inputs. (I haven't researched that as I don't have any gear that uses TDIF.)