We would be foolish to expect anything, in my view. The ways that subsidiary churches / chapels of any sort are recorded cover just about any option. Sometimes they appear in the parish register with just individual annotations on a case by case basis, sometimes specific pages within the main PR, sometimes in their own register. Throw in Bishops' Transcripts and Archdeacon's Transcripts and you have to look carefully to tell just what you've got. I couldn't see the images in question so I can't comment on the specifics.
Addendum: I've now had a look at the first image but the second is still unavailable. The first one (see entry 486 on page 61, image 340) is supposedly 27 Oct 1863 at St John's Church but the TNA article says "St. John's church was set up in 1877" (my emphasis). Therefore we can't trust the FS index entry - it surely has to be St. Mary's, after all.
So while your question is a valid one, those particular two entries don't help (the 2nd image might be just a duplicate of the first?)
The only entries that I've found for St John's start on this page 100, image 587, entry 793. It appears to be described as Item 19 "baptisms at St. John's, 1892-1901" and is the only St John's item that I saw in the FS Catalogue for Littlehampton. One entry on p.101 is for Herbert James Collins, baptised 9 Oct 1892 but the index simply says "Littlehampton, Sussex, England, United Kingdom" even though the previous page is headed "St. John's". I could only see one index entry for that (i.e. no duplication) but that could equally imply indexing problems.
What I'd not twigged before is that page 100 (St. John's) appears to be in the middle of a baptismal register for Littlehampton - presumably St. Mary's. The prior page (p.99) finishes with entry 792 and has a hand-written note at the foot saying "Continued on page 14x" where the "x" might be "0" - these (presumed) St. Mary's entries are blanked out by sheets of card - presumably they fell outside the permitted dates. The continuation pages are not on the published film.
My conclusion is that these St. John's entries were actually written inside the St. Mary's register in a pre-determined set of pages (p.100 onwards). Whether there are any other St. John's entries, I don't know - nothing else appears for St. John's in the catalogue.