Perhaps some of the more math inclined peeps can set me straight here. Apologies if this seems like another one of my "streak" threads; I'm not intending it to be!

What I wonder, what does one think of when they hear "batting average?" I know stats like BA, OBP and whatnot are sometimes referred to as "rate stats" but do they really measure rate or do they just measure average after the fact?

For example:
If a player has a .300 average and comes to the plate 10 times does that mean he'll get 3 hits?

OR

If a player has a .300 average and comes to the plate 10 times does that mean he has a 30% chance of getting a hit in each plate appearance?

AND

Is there a difference?