Ric-
No, the software you're talking about is all-in-one type stuff. You won't be recording files in one app and then mixing in another.
I don't know about any other versions of Cakewalk, but Cakewalk 9 Pro and Sonar are full-on multitrack recording suites. You would record your tracks into Cakewalk, and then do all your EQ, effects, pans, etc. in Cakewalk. You may or may not use other "utility" type programs to assist.
For example, I recorded our last album to ADAT, digitally dumped it all to Cakewalk, and then mixed it all down. While mixing, I would jump out to SoundForge (via an option in Cakewalk) to apply various plugins for EQ and fx. Then, I'd refresh the file in Cakewalk and adjust level and pan accordingly. Then, when finished with the mix, you use the handy Mixdown Audio feature to throw your song out to a 16-bit, 44.1 kHz WAV file. Voila, CD-ready audio.
The same thing holds true since we've moved to Nuendo: I record all tracks direct into Nuendo, and I find I never have to leave it to do all I need (eq, fx, etc) because it can see and use all my plugins and has great built-in EQ and FX of its own. That's why I use Nuendo -- because I can mess with the sound of each track as I listen to playback. With Cakewalk, I could only make changes with the track essentially soloed -- which resulted in a lot of time-consuming trial and error. I understand Sonar is more like Nueno in that respect.
So you will just need a primary application like Nuendo, Cakewalk, Cubase, etc. to do the bulk of what you're after. Additional programs needed would be more like a SoundForge (for "mastering" or editing your stereo mixes), or various plugins like Waves for FX and EQ processing.
The greatest thing about mixing on a computer? One word: automation.
EDIT: BTW - Fletch is right, there is a learning curve with these programs. With great power comes great responsibility, Peter. The way to learn it is to start messing around with it and see if you can record something.