The present progressive (also called present continuous) is a tense. For example, the sentence “I am running” is in the present-progressive tense. The verb is in a so-called finite form
The present participle is not a tense, but a form of the verb. For example, just the word “running” is the present-participle form of the verb “to run”, which is here in a non-finite form.
A verb in a finite form has the mood, tense, and person clearly defined. For example, in the sentence “I am running”, the verb is conjugated in the indicative mood, present (continuous) tense and first person singular. OTOH, a non-finite form of a verb is independent of mood, tense and person.
Finally, a gerund is a noun formed by using the present-participle form of a verb. For example, in “the running was done by me”, the word “running” is a gerund.
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