Why would one have a private baptism?

An ancestor of mine was born out of wedlock, having been baptised on 5th April 1807 whereas his parents married on 12th October that year.

His baptism reads:

“Robert the son of Mary Littlewood single woman was born April the 3rd privately baptised the 5th.”

I’m not sure if a private baptism had to do with being born to unmarried parents. I’m also surprised that no terms such as “base.” or “wedlock,” or “natural” was mentioned as normally seen with other ancestors of mine born to unmarried parents.