In linguistics (and more specifically, morphology), two similar but not quite equal processes apply whereby words that are semantically-related to each other can be developed from one another.
Inflection is the process where a word is changed subtly or slightly to reflect grammatical information. Different conjugations of a verb (eg. "I walk" versus "she walks"), or a plural form of a noun (eg. boxes versus box), are examples of inflection. It is important to note that an inflected form is still considered to be a form of the same word.
Derivation, on the other hand, is the process where a new word is created (or derived) from the root form of another word. Examples include an adjective being derived from a noun (eg. childish derived from child). The distinction from inflection is that with derivation, the results are considered to be totally separate words, rather than forms of the same word.