The Gemara in Chaggigah (4b) mentions a woman by the name of Miriam Megadla Se'ar:
זיל אייתי לי מרים מגדלא שיער נשייא
Which means she was a "grower of woman's hair" which is to mean she was a hair dresser.
When I came across this I thought for sure this is a reference to Mary Magdalene of Christian fame. She is also the patron saint of hairdressers (SE.Christianity site featuring our very own Mi Yodeyan:-)). So I thought for sure the Gemara is talking about the same person. As both the name and profession seem to line up.
However, Tosafos on the Daf says instead this is Jesus' mother Mary.
דמרים מגדלא נשייא בבית שני היה דהיתה אמו של פלוני
I was wondering is Tosafos correct in their identification? Were the Baalei Hatosfos familiar with Christian theology and works to be able to correctly identify Mary?
Are there any sources which discusses this?