Z53C80 and NCR53C80 are the same part from different manufacturers. Often, one manufacturer will license the part from another. In some cases, they develop the part independently, but with the same functionality and pinout. In those latter cases, one should compare the datasheets, because sometimes there are subtle differences which turn out to matter.

In this particular case, The Z means that Zilog made the chip. NCR means that National Cash Register (before they's chip division mutated into SYMBIOS*) made the chip.

*Later, SYMBIOS or part of its library was bought by LSI Logic, so ultimately, what started as a NCR53C96 (related, later SCSI chip) finished its production life as an LSI53C96.