No one knew how to spelled their names. The priests (and census takers, etc) just spelled everything phonetically. You may say Fisk today, but who know what it sounded like in German, which is likely the language being used. The DAR people who work with the applications understand this.
The church is the same, although the reference to simply "Reformed Dutch Church" has little meaning. There are scads of those in NJ. I'm sure it's the same person. I misread your first message and thought you were saying James was the father of John. That's what made me ask for the name of the church.
I checked another source I have and Peter Fisk had two more children baptized after John in another church - Harlingen Reformed Dutch Church, Montgomery Twp - which is also in Somerset Co. You will find these records abstracted in the Genealogical Magazine of NJ, vol. 16 & 17.
Ragel bp. 6 May 1760; parents Pieter Lisk and Catryna.
Marya bp. 25 Jan 1761; parents Peterrus Lisk and Marya.
Peter apparently had a 2nd wife.
Montgomery Twp is some distance from the first church, suggesting they may have moved. The Harlingen church borders Mercer Co, while the first church is closer to Hunterdon Co.
Regarding contacting the churches, they are likely to tell you the records have been abstracted and are available. I looked through the 1791 records for both churches and don't find any entries resembling your James Lisk.
I did a quick google search and found an e-book showing John Lisk died in 1823 and was buried in Monmouth Co. He apparently moved around a lot.