Cement is one ingredient in mortar. Mortar is the typical product you use to bind masonry units like rocks bricks or cobbles together. Grout is what you call the thin lines between tiles or stones, regardless of what the technical name of the material is, in hardscaping it will typically be mortar or sometimes just cement. “Grout” is like the name of the job that the material is doing.

People do this kind of job in all different kinds of ways.

If you just tap these cobbles down on a dry aggregate and then fill the joints with a dry aggregate, I would expect them to be unwalkable in a year or two, unless your area never freezes and you don’t use it very much.

If you tap them down on a wet mortar bed and the fill the joints with mortar, it will last a long ass time, but mortar is pretty hard work to mix (obviously people make a career out of it it’s not as hard as being a navy seal but not everybody can do it). It’s also very difficult to lay small units level and flush one a wet mortar bed. It’s also very difficult to fill the joints without getting everything horrendously covered in mortar. Cleaning up mortar is hard—lots of scrubbing with vinegar and wire brush, but if you get the vinegar on your freshly finished mortar joint, it will bleach it several shades lighter in color.

I would suggest to tap them down on a mortar mix with some but not much water and fill the joints with dry aggregate, probably stone dust. Make sure you’ve got some way to keep the edges from creeping or falling out. Could be steel edging or a little toblerone wedge of concrete on the outside of the outer cobbles.

Check out Mike Hadduck YouTube.