Etymology was the term used for both concepts up to the early 20th century. Then de Saussure postulated the incompatibility of diachrony and synchrony and nothing was ever the same again.
Etymology is a study of the history of words' form and/or meaning, and history implies diachrony. Thus, the word lord comes from Old English hlafweard "one who guards the loaves". During the centuries the form of this compound word changed (the two parts of the compound merged into a single stem), and also the meaning evolved into something different. The study of such processes is the diachronic analysis.
On the other hand, morphology refers to the word form in synchrony. When we analyse a word into its constitutive parts, such that they are functional within this language and speakers are, possibly, aware of them, we do a synchronic analysis. For example, an average speaker of English knows that landlord is a compound word built from land + lord, or that lords is a plural form of lord built by adding the plural marker -s to the stem. But no speaker would ever know the diachronic origin of the word lord from its Old English prototype, without a specialist training in Linguistics.
Saussure's claim is that above mentioned two approaches to the analysis of language cannot be combined together. You can do either one or the other. In other words, you cannot describe the synchronic grammar of a language making reference to some of its preceding diachronic stages.