It's a little harder for native English speakers to remember the difference between these two forms, because in English they have the same -ing ending. But in German (and most other languages) they're formed differently.
The present participle is a way of using a verb as an adjective, and in German it's only used right before a noun, as in "running water" or "barking dogs." It’s formed by adding a –d to the end of the infinitive, then the normal adjective case endings:
Auf der A1 ist fließender Verkehr. (traffic report)
[Smoothly] flowing traffic on the A1.
Don’t confuse the present participle with the more common past participle that we’ve been discussing up till now. You can also use the past participle as an adjective, but of course it has a different meaning (think of breaking glass vs. broken glass).
A gerund is a verb used as a noun, as in "The Taming of the Shrew" or "the running of the bulls." The gerund in German is just the infinitive, capitalized. (Like all nouns.) All gerunds are neuter, and when there’s a plural, it has no added ending or umlaut.
You often see the gerund on signs, in both German and English:
No parking [literally "parking forbidden"]
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