Do graphics cards have built in HDMI out? or is that on the motherboard?

My hd7950's do.

most cards made in the last 3 years or so have hdmi, as do many motherboards that have integrated graphics. a few don't, but you can get adapters

hdmi is just a different interface for a video output much like VGA, DVI, Dual-link DVI, DisplayPort, mini-Displayport, mini-hdmi etc etc. They all vary depending on what kind of graphics card you get. Your motherboard will only have a video output on the back if the board was designed to have a CPU with integrated graphics on it (like an APU or a newere intel CPU), or has a graphics chipset built-in on the motherboard.

Most graphics cards will come with Dual Link DVI-D ports and HDMI ports. Some will come with Display Ports as well, but nothing is using VGA anymore.

thank you