I'm guessing this is a pretty straightforward question. Examples would be helpful too, thank you!
To be precise, の is a particle that can fulfill different roles (mainly: attribution, concomitancy, substitution). So の as a "pronoun" is just の particle substitutive use and not a pronoun.
So from your question, the main difference will be the role in the sentence.
走るのが好き。 (same as 走ることが好き。)
That said, there are of course more nuanced uses of の but if you can clearly understand and use these 3 roles, you made the hardest part.
Well, "A dictionary of basic Japanese grammar" has a special paragraph about it. It gives:
In this example トムの is the omitted form of トムのペン. Therefore it's just a particle and not a pronoun.
On the other hand, a noun can't be added after の used as a pronoun. i.e.
In this case, の is not an omitted form.
Would be grammatically incorrect (The right way would be 私は黒いペンが欲しい).
の as a particle has the very simple function of noun modification. You might find some comparisons between の and the English 's or "of", however these can be a bit confusing once you start running into less directly translatable uses.
It can also act similarly to the particle が in some sentences:
の as a pronoun, on the other hand, is very simple in its most basic uses, being the basic equivalent to the English "one." The question that Andry links to addresses the nuances, but most of the time you'll be fine associating it with "one" in English, or something similar to a possessive pronoun like "mine." For example:
There are some grammatical rules to it, like not ending the sentence with the pronoun の. Grammar dictionaries are great for the nuances.
Please consider my answer to This question.
Both the question and my answer (and other answers as well) will redirect you to very interesting content and useful grammar aspects regarding your question.