Electronic – Is TMDS really differential

"Ground" as a concept needs some clarification. If you have just one signal line and one ground, then yes, it's hard to tell the difference. But if there's anything else going on, it matters.

All AC signalling involves current flow, even if it's being measured as a voltage on the receiver. At a minimum, you have to charge/discharge the parasitic capacitance of the receiver, and the signal wire will have a capacitance to ground as well. Note that the common mode behavior only holds if the two wires have the same length and are a constant distance from each other.

So if you have a signal wire and a ground wire, then the current in the signal wire must be matched by a corresponding current in the other direction in the ground wire. If you have lots of signals, the ground wire will contain a mashed-together copy of all the signals. Therefore it's advantageous for each signal to have its own ground. If you look at VGA, you'll notice that each signal gets its own ground because of this. If you look at 80 pin IDE, each pair of signals has a ground wire between it in the ribbon cable. Those are to prevent the signal wires inducing currents in each other ("crosstalk").

Once you've accepted that each signal must have its own matched ground, it's more natural to embrace the two as a matched pair, disconnect one from ground and connect the two of them together via a termination resistor network, and drive / read them as a differential signal.

Good questions. I have been researching this topic myself recently, and will try to provide some brief answers here.

what exactly is TMDS vs LDVS?

LVDS (low-voltage differential signaling) is simply an electrical specification for a differential signaling interface, while TMDS (transition-minimized differential signaling) is both an electrical specification AND a specific 8b/10b encoding scheme. Unfortunately, the electrical specifications are not directly compatible, although there are various ways to "adapt" one to the other under certain circumstances.

Electrically, LVDS uses totem-pole drivers and differential termination (100-120Ω), while TMDS uses CML (current-mode logic) open-collector drivers and individual 50Ω terminations to +3.3V. The Spartan-3E IOBs do not directly support CML.

Then there's the question of TMDS coding. The Spartan-3E IOBs have support for DDR, with data rates up to 628 Mb/s, but no dedicated high-speed SERDES logic. You would have to do the TMDS encoding and decoding in the FPGA fabric, using the DDR support in the IOBs to get the final bitstreams. This would limit you to pixel rates of 62.8 Mp/s or less.

In a practical sense, I am wondering if I can simply wire an HDMI breakout board directly to the input pins of my FPGA, configure those pins to the LVDS IO standard and expect it to work

No, not on the input side, at least not without some effort to terminate the TMDS properly and then AC-couple it with proper bias to the LVDS receivers on the FPGA (all of this while maintaining an accurate 100Ω differential impedance). Note that the sample projects you link to are all output-only examples. Driving DVI/HDMI from an LVDS output seems to be much more forgiving; they don't seem to have added any bias or termination resistors to their PCBs.

Your best bet would be to use external DVI/HDMI input and output chips, and make the connection to the FPGA via their parallel buses. I have used Analog Devices parts in the past.