I was taught that the Present Continuous is formed using the Gerund, but that you call it the Present Participle. Even though these two forms look exactly alike in English, in other languages they do not. Can you explain this discrepancy?
Historically, English had a gerund form and a present participle form, which often looked and sounded different. Over time, these converged, so that they now look and sound the same. Because of this convergence, some linguists argue that there is no difference at all anymore. The Cambridge Grammar of the English Language, for instance, calls the -ing form of the verb "gerund-participle".
I agree that since the two forms in English are now identical, it doesn't make a lot of difference what you call it, but a good bit of our grammar was inherited from Latin and in Latin, the continuous (sometimes called progressive) forms used the gerund and not the present participle. If you want to call it gerund-participle, fine, but don't call it present participle. Some Latin languages, such as Spanish, do not have a present participle. They have some adjectives which take the same form as the Latin present participle, such as "interesante", but Spanish grammar has no element called a present participle. They do have continuous forms in their conjugations, though, so they must use the gerund which, using the same verb root, would be "interesando". Italian, on the other hand, has both present participle and gerund (interessante and interessando, respectively), but they still use the gerund for the continuous forms. I realize that the evolution of English is not dependent on any other language, but there is no reason to make such a switch in terms.