Any type of sugar that is cooked to a brownish color can be called caramel. The taste of caramel will naturally take on the taste of the type of sugar you use. You can make caramel with white sugar, brown sugar, honey, glucose, corn syrup, condensed milk… you can even make caramel with soft drinks like coke or root beer… as long as there is a high sugar content, it can be caramelized. The color of caramel depends on how long you cook it. if you want a darker color, just cook it longer. if you want the caramel to set harder and thicker, cook it at a slightly lower temperature for longer, so that more water evaporates.
The most common type of caramel you’re probably thinking about is just made with normal sugar, that has some cream added to it at the end, but there’s a whole world of different possibilities out there to try :)