"tubs" are tubular tyres. These are a full circle in cross section, and are glued to a rim that has no flanges. A tub has a tube sewn into the inside of the casing. You have to unpick the stitching along the underside where it is stuck to the rim in order to get at it.
I must say I wasn't aware that there were any MTB sized tubs.
A tubeless tyre has no inner tube, and has a bead shaped so that it forms an airtight seal against the rim. You also need a rim with no spoke holes in the rim bed, and preferably with flanges that match the tyre bead.
It sounds like this is what you mean.
See
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