Is it the same discussion as lag baomer that falls out on Sunday?
No - there seems to be a chiluk dirshu brings down that because everyone knows that you can take a haircut on sunday as its shloshes yimei hagbalah so its not a bizoyon if you shave on sunday vs on lag baomer its not as known /mdrabanan so if you see a person takes a haircut on sunday and not shabbos it can be a bzayon for shabbos. I am not sure if that is the reason of R moshe or R Elyasiv they just bring it down that R shlomo zalman is not choshesh for the above.