Salves, Balms, and Ointments are all medicinal preparations involving oil and some sort of hardening agent, often a wax or resin. From there every medicine maker and their herbalist cousin may have a slightly different view. Some folks say that they are all distinctly different preparations, others that they're all the same darn thing. The one other commonality is that the oils used are often infused with herbs, or have herbal extracts added to them.
Given the folky nature of the medicine which these terms developed from, it's not surprising that they would tend to overlap or have multiple different meanings. What is perhaps more useful to think about is why you'd want to make a sticky, oily medicine in the first place.
The whole purpose is to get your herbs in a medium that will adhere to the skin long enough to have a healing or protecting effect. That's it. From there it's all semantics and how much beeswax you add. Below we've outlined a few of the common definitions surrounding these terms. But remember, it's not always cut and dry (in fact, it's often a bit sticky...)
An oily medicinal preparation for healing and relieving skin complaints. Salves can be soft to hard, but tend to be of a medium hardness. Sometimes considered interchangeable with 'ointment'. The term has two potential origins. In Latin salve meant "good health!" and was used as a greeting. In sanskrit sarpis meant "soft butter", possibly alluding to the consistency of a salve.
Another oily medicinal preparation, but usually thought of as a bit harder than a salve, and tends to be aromatic. Think lipbalm, tiger balm, etc. Sometimes considered interchangeable with 'ointment'. The word balm has it's origins in the Latin balsamum, Hebrew basam and Arabic bašām, all of which refer to the term "balsam". Balsam is the 'ye olde' term for an aromatic resin which comes from a plant.
Yet another oily preparation for soothing the skin, but usually thought of as a bit softer than a salve or balm. Think of a salve with a lotion consistency and your on your way. Sometimes considered interchangeable with 'salve'. The word origin comes from the obsolete Old English verb 'oint' (to anoint), and Latin suffix 'ment' (which implies an action or result).