Tough to find a map online that shows both. This one will have to do for now.
The main map shows "the strip" - the section of Las Vegas Blvd that has many/most of the bigger, big name hotels and attractions.
The hotels along the strip tend to be nicer, posher, more "Vegas-y", and not surprisingly, more expensive. There ARE cheaper ones there, but you may have to do some hunting.
The blue dotted line indicates the path of the monorail. You'll note as it goes north, it curves off of the strip and runs behind it a bit, stopping at the Hilton and other places. These hotels are considered "off the strip" - they're close enough to the strip that you could walk to it if you desire. These tend to be a bit cheaper because of that, although again, you'll want to shop around. The Sahara is technically "on the strip", for instance, but since it's at the north end away from many of the "hip" places, it's usually on the cheap end. Whereas the Palms is off the strip, but since it's rather trendy, it'll be a bit pricier.
"Downtown" is also (or used to be?) called "the old strip". It's located a bit of distance from the (new) strip. Not sure of the exact distance, but it's a bit a of a walk. It has the older hotels, and it's what used to be the center of Vegas. If you know that U2 video for "I Still Haven't Found What I'm Looking For", that's where it was filmed. They've revamped it and made it a bit hipper, but it's generally cheaper than hotels on the strip. However, you'll be a bit removed from most of the attractions, and you might end up taking a cab over to the strip, so factor that in.
Lex