I can give you the Italian answer - first of all, normally we don't use tomato paste to make sauce, but rather to add a tomato "kick" to recipes. Tomato paste is simply tomato puree that has been cooked down to a high degree of concentration.
A basic tomato sauce is made by
- making a soffritto with onion, carrot and celery (plus other flavors)
- adding tomato puree, or "pelati", more rarely fresh tomato
- cooking the sauce down until the taste and thickness is what you want
If you want to use paste instead of puree, the third step has to be omitted or greatly reduced in duration. Keep in mind that tomato paste has its own taste, and that taste will remain in the final sauce.
A standard tomato implies that there is a standard salsa, which there isn't - but let's stick with your specific case of pico de gallo AKA salsa cruda.
The distinguishing characteristic of salsa cruda is that it uses raw tomatoes - the cruda literally means raw. Since you aren't going to be cooking them, and since water is going to be your primary binding agent, you'll want to use plump, juicy tomatoes that have potent flavour when raw, and that just so happens to be those bog-standard globe tomatoes you see in the supermarket aisles. Of course, if you can get garden-fresh tomatoes, so much the better.
Cherry tomatoes are also a great choice - they're very juicy and a little sweeter than globes - the only downside is that for a chopped salsa (as in pico de gallo), they tend to make preparation much more difficult and messy. If you've got the time and patience, give it a try; cherry tomato salsas taste much "fresher" than those made from globes.
The other common types of tomatoes, most notably roma and pear tomatoes, are really meant more for cooking. That's not to say you can't eat them raw, but they don't have a lot of juice or raw flavour, so they don't make a good base for cruda. Roasted roma or heirloom tomatoes (especially fire-roasted) make a great addition to salsa, but of course, it's not really "cruda" anymore if you cook any of the ingredients.
Do yourself a favour and don't use the plum tomatoes in a can; they're plenty juicy but have almost no seeds and no flavour.
So, all in all, for pico de gallo I believe that regular globe tomatoes are the most appropriate, but any tomatoes with strong flavour and plenty of juice will do.
Best Answer
Tomatoes contain high levels of glutamic acid and its sodium salt (mono sodium glutimate or MSG). In fact, the pulp contains over 4 times as much as the flesh of the tomato. In a tomato paste, the concentration of glutimates is even higher. The "unique" flavor is not only concentrated tomato, but the umami that comes with it. Tomato paste packs a very high umami punch that distinguishes it from fresh or canned tomatoes.
By the way, next time someone suggests that they want to avoid MSG, ask them if they also avoid tomatoes, Parmesan cheese, soy sauce, and many other ingredients where it is naturally occurring. Lot's of good info here.