Location of Ancestor's parish church - St. Mary's, Cork City

Hello,

I am researching my O'Connor/Connor ancestors from Cork city, Ireland.  Jeremiah O'Connor and Catherine Twohill (sp?) had several children, one of whom was Dennis Patrick O'Connor baptized 15 Dec 1872 at St. Mary's in Cork.  At the time the family lived on Fair Lane, which I understand today is Wolf Tone street.

My question is does St. Mary's refer to the cathedral of St. Mary and St. Ann shown here - https://www.corkcathedral.ie/ or does it refer to another St. Mary's and, if so, what is the location?  

Thanks!

Colleen Kennedy