Yea, about the same grit size.

But diamonds will finish differently, than a stone. 1um diamond will cut more aggressively/deeper than a 14k grit stone.

So, while the grit size may be the same or close, performance may vary. For example, .50um Chrome Oxide, .50um Diamond paste, .50um CBN and a 15k stone will all leave very different stria pattern and edge.

Diamond the roughest, CBN the smoothest, the same for the edge. Ironically .50um Diamond would easily revive an edge and .50um Chrome Oxide and CBN polish it to a very comfortable shaving edge.

Depends on what you are trying to achieve.