Look closely, they typically are NOT the same plug.
They have the same circumfrence, but the pin layout and especially the "key" (the piece of plastic used to ensure you have it aligned correctly) is different.
A real "S-Video" port has 4 pins, plus a "tangental" rectangular key whole, plus 3 dimples in the plastic to assist in alignment in mating with 3 matching indents in the metal plug. The wires are two pairs: Ground+Chroma (picture color), Ground+Luminance (picture brightness, or the b+w picture).
Here's a good picture of a s-vid port:

Video cards usually use a port similar in size but with more pins to handle additional signals such as Video Composite In, Video S in. The key usually is vertical instead of horizontal, and more pins are placed in different positions. I can't find a picture of one right now to compare with.
Usually these cards will include a breakout "Y" style cable that plugs into that port that fans out into all the different connectors it supports. The small round plug is only used for connection convience and to save space on the card instead of mounting all the individual ports on it that it may not have room for (or cost more with pc board extensions/etc..)