"Seeing" - You physically see the crater on the moon.
"Calculating" - you don't actually see all of the craters, but you can infer, based on various new deposits/splotches of ejecta, that in the time reviewed, that approximately 222 new craters were created on the surface of the moon.
The difference between the two, is that in the case of seeing 222 craters, it leaves open the possibly that many others, particularly on the "Dark Side" also occurred. In the case of calculating, it may be the case that they are suggesting that a total of 222 major craters were created during that window of time.