Bogár is "beetle" and I'd say the situation is about the same as "beetle" versus "insect" in English. Most people more or less recognize a beetle when they see one and will probably use the more specific term if it's appropriate, even if they can't give a precise definition of the difference between the two. Likewise bogár and rovar.
Technically, "bug" and "beetle" mean different things. http://www.naturallynorthidaho.com/2014/09/whats-difference-between-bug-and-beetle.htm