Is there a difference between being penalized in Google and being banned?

Right now i have a client, in which no matter how many links i build or how well optimized the site is, the high priority (medium to high volume) keywords won't show up in the SERPs at all.

I know the site is not banned.

The site is 3 yrs old and has almost 3000 backlinks.

a month ago it appeared on the 1st and 2nd pages for high volume keywords.

I think the site has been penalized but not completely dropped from the index. Which would explain why it ranks for very low search volume keywords and its company name only.

I've also been told that if you're penalized, then Google will completely drop you from its index. I thought this was called banned...?

Is it possible that a penalty can also mean (or just means) that Google will push your site out of the top 100 or so for competitive terms but still index your site?

There's a big difference. Banned means you're gone, as in site: shows no more pages and your toolbar is dead. You don't rank because your pages aren't even in there.

Penalized means you're still indexed, you just don't rank anymore.

is it possible that a site can be penalized for certain keywords but not others?
or
when a site is penalized, is it penalized for any and all keywords?

I'm asking this cause all of my client's rankings for its most competitive terms disappeared in a day (they had top 30 rankings for 20 or so extremely competitive terms ie. 2,000+ searches/day), however, it still ranks for its name and non-competitive terms (less than 30 or so searches/day).

Yes, this happens. I'm not sure the terms are "penalized", as such. But they appear to be. You used to rank highly for a phrase and now it's in position 200. This could also be that something that used to boost your ranking in the algo has been eliminated or changed.

This is a weird situation that has occured to me several times. I noticed some term "popping in" again last night, in the same spot.