What's the difference between Swell, Waves & Seas?

Seas are created when the wind blows on the surface of the water, creating movement. With enough wind over a large enough area for a long enough time, swell forms, which become organised, well spaced patterns.

The swell then travels until worn out by time, distance or obstacles. Generally, "Swell" refers to open ocean waves, "Waves" are what people want to go stick their surfboard on.

Seas can sit "on top" of a swell, and ruin a surfers day out.     They are the localised chop, that given enough time and wind energy would ultimately turn into swells.

An example:

Consider a nice windless day & you're looking at your local surf break.  

6 foot swell, no wind, no seas:
What you'll see is a surfers dream.   A milky smooth water surface and crystal cylinders.

6 foot swell, no wind, moderate seas:
The swell is still solid, but you'll notice that there's no milky smooth water surface any more.  There'll be chop, and wavelets mucking up the waves.

So, seas are the smaller waves/chop that are present within the swell.  Depending on how they're generated, depends on how much it can take away from a surfers day.