Is CoA-S-R the same as CoA-R, and is CH3C(=O)CoA the same as CH3C(=O)SCoA? Eg. Above is the compound on the right just coenzyme A or is it actually another compound and not just notation?
To understand the nomenclature here it is very helpful to think about how Coenzyme A works. It has a thiol group (-SH) which can form a thioester bond to an acyl group.
So the sulphur in "CoA-S-R" is part of the CoA, and in "CoA-R" the sulfur is just not explicitly named. Those two mean exactly the same thing: Coenzyme A linked to R via a thioester on the thiol group.
One specific variant that is very important in biology is acetyl CoA. The chemical formula you mentioned (CH3C(=O)CoA) is acetyl CoA, and here the same as above applies and the sulphur is explicitly mentioned in the second one and implied in the first one.