I believe it has to do with thickness of ink depending on what medium. But a good question as to be honest I am not entirely sure myself. Perhaps more readers will contribute their knowledge and opinions about this for this post?

“Relief” inks might refer to something like the Speedball water-based block-printing inks. They can be used for making linocuts and other relief prints, and for monoprints. They’re not waterproof but they’re easy to work with and easy to clean up. I haven’t used etching inks but I gather they’re quite viscous and presumably oil-based. Speedball and other manufacturers make oil-based block-printing inks too, so it might refer to these.

there are oil based and water soluble veg. oil relief inks on the market
Caligo (from Wales) make a flax oil relief printing ink that can be cleaned up with detergent and water.
Faust Inks (New Jersey USA) manufacture a veg. oil relief ink that can also be cleaned up with detergent.
Akua Intaglio ink can also be used for relief printing. It is a soy oil product.
Gamblin have a relief printing ink..traditional linseed oil I would believe as it can be cleaned up with odorless mineral spirits.
Charbonnel have a new line of ink called Aqua Wash that can be cleaned up with detergent and water.
I have also used a Graphic Chemical glycol base relief printing ink that washes up with soap and water. However although I was told these are waterproof when dry I did not find that to be the case.

Hi, You are correct about the process of making etching and relief prints. The part of the relief print that does not get carved away, receives the ink from a brayer or roller, and printed onto the paper, essentially. With an etching, the reverse is true: the lines that you etch into the plate receive the ink by wiping the ink across the plate and ‘pushing’ the ink into the grooves. The paper (usually dampened) is then laid over the plate, and pressed ‘into’ the grooves of the etching plate, thus picking up the lines of ink.

Viscosity refers to stickiness or “tack” which allows the ink to stay in place, and not ooze or run off the surface of the relief plate (or out of the grooves of an etching). I am using oil-based, water soluble etching and relief inks. Bridog made a good list in his post above. They perform much like straight oil-based inks and the better inks -in my experience- are similar in thickness and tack, but have easier clean-up and no fumes. (My cats hang out in my studio and I don’t like using anything toxic!)

I can’t imagine thinning the inks for any reason for a relief print, however. The amount of ink on the relief plate is controlled by how you roll out the ink on your glass inking plate, and then how evenly you apply it to the relief surface. You don’t want it to be runny or thin.

Again, that’s my experience with the water soluble etching inks. The pure oil-based inks may be more apt to need thinning. Someone who uses these inks more frequently, may have better info about this.

So, to your original questions -in my experience “etching inks” work for both relief and etching inks, straight from the tube or can.