What’s the difference between tactile and tangible? Very little—and they are cognate, sharing the same Latin source—but there is a subtle distinction in their use.
Tactile, from the Latin term tactilis, by way of the French word tactile, and ultimately from the verb tangere, meaning “touch,” refers to things that can be touched and to the action of touching. For example, very young children, who learn about the world by manipulating objects, are said to be highly tactile. Unlike tangible, tactile does not have a direct antonym.
Tangible, meanwhile, also derived from tangere, pertains more generally to things that can be touched. A tangible reward, for example, is something that can actually be handled, such as a trophy, as opposed to an intangible reward, such as an accolade; the word also applies to things that can be realized rather than simply conceived of. (Like, tactile, it has an intermediate and identical French form; it comes from a Latin noun derived from tangere that refers to touchable things.)
An etymologically unrelated but similar-looking synonym is tractable. It’s most common sense is “manageable,” but it can also mean “touchable.” Its antonym, intractable, refers to a problem (or a person) that is very difficult to manage.
A handful of additional words have similar meanings. Palpable is a direct synonym of tangible but can also simply mean “obvious” or “unmistakable.” Perceptible means “able to be noticed with one’s senses.” Appreciable and ponderable both have that same meaning and an additional sense of “measurable.” Sensible also applies to what can be perceived but has additional related meanings, as well as pertaining to having good sense. Manifest has literal and figurative senses, pertaining either to something clearly shown or visible or to something easy to recognize or understand. Only palpable and sensible have direct antonyms (impalpable and insensible).