Balm is a strange word. It just feels weird in your mouth. Balm. Try saying it aloud.
There aren’t many words which sound quite as peculiar as balm. And don’t say palm, or calm, they don’t count. It’s that open mouthed ba sound which has to wriggle back to the lm. Balm. Sounds like you’re still learning to talk.
I’ll give you a little history. Βάλσαμον (or bársamon to us English speakers) is an Ancient Greek word which refers to the Arabian balsam tree, and the fragrant oil which it produced. They borrowed part of the word from Hebrew, בָּשָׂם (bāśām, “sweet spice, sweet smell”). When you start down the rabbit hole of etymology, this becomes a very, very common trend. Always borrowing.
Once Latin entered the party, we ended up with balsamum, which in my opinions sounds like a little serving of salmon drizzled with balsamic vinegar. I’d eat it. The meaning was exactly the same, they just decided to complicate things. Then time passes blah blah the Old French get their grubby hands on the word and we arrive at basme. The Gaulish (I don’t know who they are either) arrive to their own conclusion and balma. The era for Middle French begins and the conversion of the two leads to baulme. I like that one. Baulme. Very soothing.
What would we do without the English, they enter the scene and decide things don’t need to make sense to be part of the language (Now that’s a running theme) and we get the oddity which is balm. By now the word doesn’t reference so much the tree, as just something soothing, or the aromatic product of a plant.
If you do a deep internet dive, there are links between balm, and resin. Lemon balm is a herb. And you can buy things like beard balm, or lip balm, or tiger balm. Some brands do eye balms, and flash balms, and general face and body balms.