Each form has lexical meaning. Here, they are coterminously a root and a stem. Roots are also bases. A base may contain affixes, a root cannot: car, book, buy, etc. are roots and stems. pre-fer, ...
Gerunds are the -ing form of a verb, and infinitives are the to + base form. These words can be confusing; they combine the meaning of a verb with the grammar of a noun. My father asked me to ...