Certain people were authorised to perform a Private Baptism free of charge, such as Doctors and Midwives, and since it didn't involve the Church they would not be recorded in the Parish register. When the child first entered the local Church the Christening ceremony would not include the Baptism if evidence of a previous Christian Baptism was provided.
As already suggested, I suspect the date of the Private Baptism has been entered wrongly, or even very badly, and should be 1830.
Colin