It sounds like you are asking about different types of canned tomato products. As others have said it's a matter of taste, texture and convenience. Here is the 25-cent tour.
Whole Peeled Tomatoes are the least cooked and processed, and many believe have a "fresher" taste. You can use them like fresh tomatoes to dice, crush, puree, etc. when fresh tomatoes are out of season.
Diced Tomatoes are whole peeled tomatoes that have been diced and generally contain seeds.
Tomato Sauce is whole peeled tomatoes which have been run through a seive to remove the seeds, more watery than tomato puree, and is also generally seasoned with onions, and/or herbs.
Tomato Puree is like tomato sauce, but is not seasoned and is cooked a little more to thicken it - sometimes the tomatoes are run through a press to remove some of the liquid before seiving and the final cooking.
Crushed Tomatoes are whole peeled tomatoes that are simply crushed - the texture is not as uniform as diced tomatoes.
Stewed Tomatoes are basically crushed tomatoes that have been seasoned with onion, celery and green bell pepper.
Tomato Paste is the most processed and undergoes the most dramatic flavor changes. Generally, it is tomato puree which is cooked for a long time to reduce it down to about 1/4 of it's original volume. This process gives it the most pronounced cooked flavor - and greatly concentrates the flavor. It is used to add a concentrated tomato flavor to a dish with a minimal addition of liquid.
Types of Tomatoes used for canning vary - but here in the US generally are the ordinary common garden varity round "slicing" types unless otherwise specified on the label. The "sauce" tomatoes are the pear shaped Romas, aka Italian plum, etc. These are meatier, sweeter, lower in acid and less watery. Of course, they usually cost a little more. My favorite is "San Marsano" imported from Italy - WOW what a flavor!- but they cost 3-5 times as much as domestic brands.