Not too long ago Glen put it best... and I am going to paraphraze it:
Cut to fix it, boost to spice it up 
Hope you don't mind Glen! I know those were not really your words, but essentially it captures what you were saying
I don't mind, since I am not the author of the idea; it's an old truism that's been around probably longer than I have.
The way I remember it and usually state it is, "use EQ cut to make it sound better, use EQ boost to make it sound different".
I usually like to pair it with another truism: "cut narrow and deep, boost wide and shallow".
And to address MCI's confusion, which is understandable because, yes they are both "fixing" the sound; it's a reminder that surgical subtractive EQ is great for removing what sounds bad, improving the sound of an instrument without really changing it's basic nature much. Things like removing instrument resonants or other colorations that tend to over-influence the sound of the instrument or make it hard to fit into the mix.
EQ boosts, OTOH, do little to remove the bad stuff. They tend to change the overall sound of the instrument, but the ugly stuff will still be in there and will still make it hard to fit into the mix.
And rarely does one sharply boost a narrow Q the way they'd similarly surgically cut; usually good sounding boosts tend to be more of a general shaping, often (but not always) meaning wider Q, and usually meaning a more gentle maximum boost regardless of the width.
Of course, none of this is true absolutely 100% of the time; but they tend to work better far more often than they don't.
G.
