Taken from Gerunds and Pronouns on this blog:
Gerunds and Verbal Nouns:
Because they are noun-like, we can think of gerunds as names. But rather than naming persons, places, things, events, and the like, as nouns generally do, gerunds, because they are verbs in form, name activities or behaviors or states of mind or states of being.
A gerund is derived from a verb by adding the suffix -ing. The result is still a verb, and it exhibits ordinary verbal properties, such as taking objects and adverbs.
Example: In football, deliberately tripping an opponent is a foul.
Here the verb trip occurs in its gerund form tripping, but this tripping is still a verb: it takes the adverb deliberately and the object an opponent. However, the entire phrase deliberately tripping an opponent, because of the gerund within it, now functions as a noun phrase, in this case as the subject of the sentence. So, a gerund is still a verb, but the phrase built around it is nominal, not verbal.
Infinitive phrase : An infinitive phrase is the infinitive form of a verb plus any complements and modifiers.
The complement of an infinitive verb will often be its direct object, and the modifier will often be an adverb.
Example : He likes to knead the dough slowly.
The infinitive verb is to knead. The complement is its direct object (the dough). The modifier is the adverb (slowly).
More examples of Infinitive Phrases:
He helped to build the roof.
The officer returned to help the inspectors.
She tells you to dance like no one is watching.