In the baptism record, Mary is described as the bastard child of "Mary Holmes". In the marriage record, she is described as "Mary Hall". The marriage was witnessed by a "John Holmes". In the baptism record of her son, Moses, she is described as the illegitimate daughter of "Alice Hall".

Current assumptions:

1. "Holmes" was the maiden name of Mary Senior (based on the baptism record).
2. "John Holmes" who witnessed the marriage of Mary Junior was a male relative of Mary Senior.
   
3. Mary Senior married after the birth of Mary Junior and took her husband's surname "Hall".  Alternatively, Mary Junior knew the identity of her father and unofficially took his surname. Either assumption would account for Mary Junior being known as "Mary Hall" at the time of her marriage to John Carr.
4. "Alice Hall of Bramham" in Mose's baptism record is an error (should have been "Mary" not "Alice"). The surname "Hall" is compatible with assumption 3.

Alternative assumptions:

1. Baptism record (Mary Holmes) is for someone else.
2. She really was Mary Hall illegitimate daughter of Alice Hall of Bramham.
3. Presence of a John Holmes at Mary Hall's wedding was a coincidence.
   

So I'm not sure whether the maiden name of Mary Carr was Holmes (mother Mary Holmes) or Hall (mother Alice Hall). I am guessing Holmes for the moment.

The marriage between Mary and John took place in 1790 in Bramham parish, the bride was from that parish, the groom was from Sherburn parish.