Oh, the confusion! Let me take a crack at clearing this up.
Some (cheap, crappy) PiP TV’s have a single tuner, but another set of inputs you can use for the PiP function. This was typically connected to a VCR, which (of course) has its own tuner. So, what you’d do is split your cable or antenna signal, send one directly to the TV and the other to the VCR. If you turned on your PiP feature you’d be watching the TV tuner’s signal in the “main” window and the VCR’s in the PiP window. You could change channels with the TV remote to change the “main” window’s channel or use the VCR’s remote to change channels in the PiP window.
Newer TV’s have two independent tuners - it’s almost like two separate TV’s in one box. You hook up your cable or antenna to the TV, it’s split internally and sent to the two tuners. Your TV’s remote can change channels in either the “main” window or the PiP window - no VCR or other device needed.
Even newer TV’s have a multitude of inputs - composite video, S-video, coax (for cable/antenna), and two tuners. The “main” window or the PiP window can be assigned to any of these, so you can be very flexible about what’s displayed where.
When you throw a satellite receiver into the mix, things get a little complicated. The TV’s internal tuners are now essentially useless (note to nit-pickers: I’m simplifying the case and disregarding the possibility of using it for cable or antenna use at this point). Your satellite receiver is most likely connected to one of your A/V inputs (composite or S-video, and stereo audio). The satellite receiver is where all the tuning happens now, and it’s only capable of receiving one channel at a time from the satellite. So there’s no way to watch two satellite channels, even with PiP, without a second receiver. What’s coming out of the receiver is only a single channel and no amount of splitters or funky wiring can change that.
If you really want this to work you’re going to want two receivers. They’ll have to be connected to two different A/V inputs on your TV. You’ll then assign one set of A/V inputs to the “main” window and one set to the PiP window. You can then change channels on each receiver independently and watch two different things in each of the windows.
This is a common enough thing that some receivers support a function whereby two identical receivers can be controlled by a single remote. It’s basically done by assigning one arbitrarily as “receiver 1” and the other as “receiver 2.” The remote then has a switch or button to select which receiver you want to control.
I hope this helps clear things up. It can be confusing at first, but it’s really all fairly simple once you get your mind around it. If I’ve been unclear about anything let me know and I’ll try to clear things up.