"Wide" refers to how many bits in a word. Some memory devices are 1-bit serial devices: it stores individual bits and you read/write them in a serial fashion. Some are 4 bits, some are 8.
If you're bringing in data from a serial port, you could store it serially on a 1-bit device, or you could assemble them into bytes as they come in and store them on a byte-wide device.
Does the device need to be FIFO or would a regular addressable RAM work? Of course, you can implement a FIFO in software using RAM by maintaining in and out pointers.
Some PIC18 MCUs have memory sizes of a few kilobytes.