Etymology deals with the origin of a word, often by tracing its development through history, and other related studies.
From Merriam-Webster - etymology
- the history of a linguistic form (as a word) shown by tracing its development since its earliest recorded occurrence in the language where it is found, by tracing its transmission from one language to another, by analyzing it into its component parts, by identifying its cognates in other languages, or by tracing it and its cognates to a common ancestral form in an ancestral language
Morphology deals more with how words are changed through mechanical manipulation (i.e. adding -ing or -ed to change the person or tense of a word's meaning.
From Merriam-Webster - morphology:
- b. the system of word-forming elements and processes in a language [According to English morphology, the third person singular present tense of a verb is formed by adding -s.]