Ridolpho,
The circle c mark is actually a concentric 00 and is an accuracy proof mark, it has nothing to do with snipers specifically. It merely signifies the barrel met accuracy standards. Every Izhevsh i own, '43 PU sniper, 1937 infantry rifle and 1948 M44, has it.
Refer to Yuschenko, 2016, pg 101. Two distinct markings. I don't believe there is a more up to date reference than Alex's book.