These are known as gerunds and infinitives and are known as "verbals". They are formed from verbs but function as different parts of speech. A gerund acts as a noun: eating, walking. etc. An infinitive is made by adding "to" to the plain present 1st person form of the verb, e.g. to eat, to walk, and can function as nouns, adjectives or adverbs. They often function as the direct object of a true verb: "I want to give you a present" or (in this case the object of a preposition) "He was arrested for stealing a watch".
I'm only able to touch upon the usage of these verbal forms, but hopefully this gives you an idea of how they are based on verbs, but not used as verbs.