Is there really any difference in the types of toothpastes?

Some differences. While they all share some basic ingredients there are some major differences, but it's relative. Some are more abrasive so they can claim it "whitens" teeth. Some have fluoride. Some only have "natural ingredients" and some prescription toothpastes can help remineralize damaged enamel. Proper brushing is more important that which toothpaste you use.
Yes. The toothpaste market is directed to patient needs. These needs include reducing decay, whitening, breath freshening, desensitizing and lubricating the mouth. Clearly each paste had specific ingredients to accomplish the goal of the application. Determine your need and select the appropriate paste. If you are unsure of which brand is best look for the ada certification emblem or ask your dds.
Very little. Most tooth pastes are made very similarly. Most contain Fluoride and some minor abrasives. Choose one that you like the taste and feel of.
Quits a bit. Read the properties listed on the packages. Choose the one that comes closest to your needs. Brush 2x/day for 2 full minutes by the clock with no more than a pea-sized portion of toothpaste. Know also that brushing only gets teeth 65% clean. You also have to floss or WaterPik daily.
DEFINITELY. There are many toothpastes available, with all kinds of different ingredients. I would consider one approved by the american dental association (ada.) look on websites for the labels on the toothpastes and the reviews.