Latin contentus is the perfect passive participle of two verbs, contineo and contendo. Neither verb is related to the other. Contineo's root is teneo, "to hold" and contendo's root is tendo, "to draw tight, stretch" (from which we get the word "tendon"). Contendo is not especially important for us right now and its sort of a complicated verb since it has a lot of metaphorical meanings. The most common meaning of contineo is simply "to hold together, surround, encompass," both "satisfied" and "within" are rather uncommon usages. The perfect passive participle's meaning therefore becomes "encompassed, enclosed," from which "that which is within" is a naturally understood implication. But contineo has a lot of other meanings as well, like "to be near" (usually with the dative or a redundant cum), "to continue," or "to restrain, moderate," all coming from the understanding of the idea of "holding together" in different forms. It's from the last meaning, "to restrain, moderate," that contentus can (generally only after the Augustan period, Cicero and Caesar almost never use the participle this way, they think of it as "temperate" or "continuous") mean "contented, satisfied." The implication is that satisfaction is a restraint of desire, and that therefore contentus becomes an obvious participle to describe it.