Sauces can be made with non-paste tomatoes, and sometimes are, but in general specialty tomatoes are used for most pastes. These tomatoes include a long list of varieties, but often are pear or teardrop shape, have fewer seeds and a dryer texture with less juice in them and a salad or slicing tomato. Personally, when I make a sauce from scratch, I tend to mix slicing, and even cherry tomatoes in to up the flavor, but one of the costs of doing this is more juice so more cooking down to get to a thicker sauce as that extra water needs removed. Often, dried tomatoes will be used to overcome this.
The seed issue is real, and will affect both taste and color. But, the truth is, some people prefer to use seeds. I do not as I do not care for the bitterness I taste with them in.
However, even when using paste type tomatoes, at the puree stage the product will normally be far lighter, more of a tomato soup color than the rich red sauce you were picturing. This changes in the cooking down process. As you remove water, not only will the taste intensify, but so will the color. Additionally, as food cooks, the chemical and physical reactions that occur, such are carmelization will cause color changes. In this case those changes tend to deepen the color. Other ingredients will also tend to alter the color, either just by being added, say carrot in come recipes, or though reactions while cooking.
Note also, many fresh sauces will be lighter, more pink or orange, than processed, simply because many commercial sauces just like other products have added color. That is, they simply add red dye. OK, "food coloring."