The darkness of a roast greatly affects its flavor profile. I'm going to tell you a bit of the why and hopefully teach you some things you didn't know.
The Different Roasts
Coffee starts out as a bean that is pale green in color. As it is exposed to heat, it becomes darker and darker. The terms light roast, city roast, half city, and cinnamon roast are all synonymous with light roasted coffee. This is coffee that has been roasted for the least amount of time. Medium, American, and breakfast roasts are all medium roasted coffee. Dark roast seems to have the most aliases with names such as full city, European, French, Italian, Espresso (typically), and Continental.
These names can be confusing because they are not always labeled as such. Some roasters choose other terminology for their roasts and do not specify the actual degree to which the coffee was roasted.
It would stand to reason that the darker the coffee, the more caffeine it contains. Well, the opposite is actually true. The longer the bean is roasted, the less caffeine it contains. That's why many coffee shops switch to darker roasts near the end of the day.
Strength is a vague term for coffee and it can be very subjective. When you taste a very bitter or burnt coffee, you may call that strong. When I taste an acidic or astringent coffee, I may call that strong. In reality, darker coffees tend to be more bold, but not necessarily stronger. Also, as we said, the caffeine content is lower in dark roasts so lighter roasted coffee is objectively "stronger" in a caffeination sense.
Flavor profiles vary greatly in the different roasts and are the primary reason one might prefer one level of roast over another. Coffee is a fruit. Therefore, it can sometimes tastes fruity. It certainly does when it is not roasted very much. Light roasts will always lean more towards fruity flavors. Roasting coffee for longer will get rid of those flavors in favor of the more smoky, burnt flavors. The current trend in coffee is to roast lighter and lighter. This is partly due to the demand for higher quality coffee beans and more attention to detail in regards to origin and sourcing. Most "third wave" coffee roasters do not have many or any dark roasts.
Of course taste is subjective so its your job to find out what you like. Try light, medium, and dark roast. Try it as espresso, drip, french press, and however else you can get it. You'll slowly find out which roasts and which countries you prefer.