In case anyone stumbles across this thread in the future, the MX28F1000P is definitely a different chip than the MX28F1000PL. I needed a new BIOS chip for a PC Chips M575 but I was only able to find the MX28F1000PL available. The original chip was an rebranded Macronix MX28F1000P as "H.T. M21084" (ID: C2 1A) as a and the replacement was a MX28F1000PL (ID: C2 11).
I've been unable to find a datasheet for the MX28F1000PL, but UNIFLASH was able to report the differences between them. In uniflash:
my original MX28F1000P BIOS chip is reported as "Macronix MX28F1000P/24V, Organization: sectored: 7x16k, 4x4k (128K)
my replacement MX28F1000PL chip is reported as "Macronix MX28F1000/12V, Organization: sectored: 8x16k (128K)"
I'm not entirely sure what that extra 4x4k is, but I suspect it has something to do with what the BIOS refers to as its "NVRAM" area. With the MX28F1000PL installed, the BIOS reports "No NVRAM". With the Original it reports "NVRAM OK". This doesn't seem to have a functional impact on the system, but it must try to store something there and can't with the MX28F1000PL.