I am familiar with the following "titles" used for different types of Jewish schools. My assumptions (correct me, please, if necessary.)
Yeshiva - a "generic" term applying to all Jewish schools of all ages. Though, in many places, I have heard this applied only to elementary schools (see below.) I gather that this word comes either yashav - to sit or yishuv - "establishment".
Metivta - applies to high schools. I gather it's an Aramaic word, but I don't know its origin or "root form" meaning.
Kolel - college and adult program. I gather it comes from the word to mean "inclusion".
Why were these different terms assigned to these different age groups? Are these terms meant to define either some behavior or mode of learning that occurs at that age? Or are there other criteria dictating the usage of these terms?
Also, when did these terms start being used?