Caffeine is a stimulant. But it is not addictive, at least not chemically. One can become psychologically dependent on its effects however. But that's true of many things, including things that are not truly addictive.
And caffeine has a different effect on different people. For most folks, it acts like other stimulants in its family of chemicals. It can, depending on one's biochemistry, cause anxiety and elevated blood-pressure.
But for some it has a soothing, calming effect. My S, S9, was at one time placed on Ritalin (it too is a stimulant), but exW eventually saw the error of her push to get him on that drug -- too many side-effects. The pediatrician suggested, instead, that S9 be given a caffeinated beverage on a regular basis -- the equivalent to a cup of coffee each day. I can say that it really does have an almost tranquilizing effect on him. People still look at me funny when I order him an occasional mocha frappuccino, but I just shrug my shoulders and smile -- it works for us.