What does "Massage with salt" mean in a recipe?

I'd argue that 'massage' is the right word in this case.

I've this technique a lot in japanese cooking -- you cut up the vegetables, sprinkling with salt as you go (so there's layers of salt in between layers of vegetables), then you really get in there and basically massage (knead?) the pile of vegetables with the salt, so that the salt not only is spread through the pile of vegetables, but that there's some mechanical abrasion happening, too. You then typically let the vegetables sit for a while, and then you rinse them off.

When people talk about 'rubs', it's often just a coating that's at most patted onto things (like for ribs), but there isn't the extended period of mechanical manipulation that you'd expect for 'massage' or 'knead'.

If you ever make sushi, I highly recommend trying it with carrots. The carrots will lose some of their crispness, so that you can have large sticks of carrots without it being too crunchy compared to the rest of the fillings. It's also useful for other firm vegetables that you're going to use raw in a salad.

This also works well to pre-wilt your cabbage before you make cole slaw -- the cabbage will give up much of its moisture that would otherwise end up in the final dish. (I think this was the first time I saw it -- on an episode of Good Eats)

Yes, this is mostly same as rub in with salt, but with a bit more intensity and physical contact with the food. While rubbing can be taken as applying one coating, massage warrants ensuring that the salt is mixed well with the food.

It's done so that the sprinkled salt is spread uniformly.

yes. In that case, the word massage (IMO) is used wrongly, rub would be more appropriate.

It does not make sense in the case of vegetables, but it sure does with meat.