"Serial" in the computer industry has essentially two major definitions:
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Compatible with the thing labeled "Serial Port" on my computer. I don't know offhand whether there is a name that defines the bit format of this without also going into other details like voltage levels and connector pinouts. The details date back to a day when such things were less "layered" in their definitions. The normal "Serial Port" is an "rs232 asynchronous serial communications port", but that's both too much and not enough to really describe it.
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Any communications protocol where the bits are sent one at a time on a single wire ("serially") rather than many at one time ("in parallel.")
The Arduino Bootloader uses (1). Since real "serial ports" have been disappearing from modern PCs (they were heavily abused and prone to all sorts of errors), current generation Arduinos use an on-board USB/Serial translator chip. This chip is similar in cost and complexity to the main AVR, so several "cost reduced" Arduino-like clones "factor" the USB/Serial converter into an external cable, leaving the board itself with the "bare" serial interface output by the converter chip.
(2) encompasses a whole lot of different and mutually incompatible protocols. SPI, IIC, Ethernet, SATA, HDLC, FDDI, One-wire, RS232, USB, Firewire, V.35, and many more.
They differ from the "Serial Port" in speed, how speed is determined (clocking),
The "ISP" port on the arduino is actually based on the SPI protocol. Using an ISP port is more difficult than using a pc-style serial port (and there are no external SPI-style ports on any modern computers...)