Or if one was measuring cupboards and was asked for the depth of the cupboard would you want to clarify the depth of the cupboard or the thickness of the (depth of the) top?
An oceanographer might use such terminology; e.g., thickness of a reef and/or depth of the ocean.
Not my specialist subject but maybe when talking about how to stitch a hem on a garment you need to consider both thickness and depth.
In the listed dimensions a x b x c, the b stands for widths ("thicknesses") or depths of some products?
It's weird because in English "thickness" implies there's something solid to be measured whereas depth implies that you're measuring space. So a pan's thickness would be the thickness of the metal, whereas it's depth would be how much water you can put in it. You could have a tough metal pan that you can use to boil a lot of water it could be 20 cm deep, but it would only be a millimeter or two thick.
So to actual Romanian knowers -- does it work differently in Romanian? Or is this a sentence that makes no sense IRL, but will teach us how to speak Romanian?
Not quite, when talking about dimensions width x height x depth, your depth would be the height of the frying pan, and my depth would be the distance across away from you. It is an abtract description of 3D objects, that you would find in order lists of furniture or whatever.
In Romanian: lăţime x înălţime x adâncime
but then, grosime (thickness, not width) does not make sense here - my bad - but I still think the example could be about this.