There's a few types of salsa -- salsa fresca (aka pico de gallo, aka salsa cruda), which is "fresh salsa" and uncooked, and if made fresh, it shouldn't be too watery (unless you add to much liquid, eg, lime juice), but letting the vegetables sit after salting will start to draw out extra liquid and could become watery.
For truly thick salsa, you have to treat it like a jam, and cook it to release the pectin in the tomato. (or I guess you could use some other thickeners ... I've never tried. tomato paste, maybe?) You don't necessarily have to cook the other ingredients, too, but I personally like roasting the peppers and onions to sweeten then up and remove some of the extra liquid. (halve the peppers and seed them, lay them on a tray cut side up with the onion cut into wedges, roast 'til they're softened, then dump into a food processor and either pulse or liquify it, depending on how chunky you like it. And the skin falls off the peppers, so I leave 'em out).
You can do the same roasting with the tomatoes, and it'll be thicker from the food processor, but you won't get the same cling without letting them cook slowly in liquid to develop the pectin. If you roast the tomatoes, I like to use plum tomatoes, as they have more "meat" to the gel around the seeds, and take out the gel and seeds.
You can add quite a lot of tomato paste/puree but this will mask the fresh flavour of your tomatoes.
I think I'd just reduce the soup down once it was made or add carrots. Carrot flavour really complements tomato soup and many tomato soups recipes require carrots. The starch will then help you thicken the soup.
Best Answer
Tomato puree is concentrated tomato. So where it is called for in conjunction with other tomato products, be they fresh or tinned, it is an attempt to increase the tomato flavour/presence in the dish without increasing the bulk or water inherent in less concentrated products.
Additionally the flavour of puree, having gone through a reduction process is somewhat different, more intense and rich than straight tomatoes.
Indeed, canned tomatoes tend to be surrounded with juice that is more reduced than would occur naturally. Which is part of why they are used against fresh tomatoes.