There are a few types of spaghetti. The most common is the regular spaghetti you find in stores, there's also angle hair which is quite common too. There is also thin cut spaghetti which is halfway in between the two in sizes and is harded to find. The other difference you might be noticing is the way the pasta is cooked. Most good restaurants will make sure the pasta is cooked "al dente." Which basically means it's not cooked completely through. If you if you would break a cooked noodle, you would notice that the very center is still white, which gives it more of a difference in texture than taste, but can be a noticable difference. There are can be other major differences in how it is prepared, but I'm guessing it's one of the two I've mentioned that you're noticing. FWIW I've worked in an Itailan restaurant for over a decade now. Hope this helps answer your question.