USB stand for Universal Serial Bus not Port. The term "serial port" simply means that the data is transferred one bit at a time over a single signal path - in that sense even Ethernet is serial in nature. The word serial in both terms implies no relationship other the width of the data path.
You are right in that the term serial-port in the context of a PC normally means an RS-232 port, but there are other serial port standards such as RS-422 and RS-485 often used in industrial applications. What these have in common is that they are implemented using a UART (Universal Asynchronous Receiver/Transmitter).
The term Universal in USB merely reflects the fact that it is not a specific device interface such as the dedicated mouse or keyboard ports found on older hardware. Similarly a UART based serial port is not device specific, reflected by the U in UART.
USB differs significantly from RS-232 in a number of ways; it is a master/slave (or host/device in USB terminology), rather than peer-to-peer, the USB device cannot initiate communication, it must be polled by the host. USB includes a low-voltage power supply to allow devices with moderate power requirements to be powered by the bus - that is also why USB ports can be used for charging battery powered devices. USB is significantly more complex that RS-232 which defines only the physical (hardware) layer whereas USB requires a complete software protocol stack.
The term COM is just a device name prefix used in Windows (and previously MS-DOS) for a serial (UART) port. Short for "communications", you can for example open a COM port as a stream I/O device with say FILE* port = fopen( "COM1", "wr" ) ;.
