Formal Name of TXRX Communication
The best answer is "TTL-Level RS-232-Style serial communications" Sometimes with additional specifiers (parity, no parity | 7/8/whatever bits per byte | 1/2/1.5 stop bits, etc...), but those options are defined in the standard.. 

RS-232, EIA-232 and TIA-232 are all the same protocol, in general. There may be minor differences in the specs, but they generally interoperate without issue. Mostly, it's just an issue of which standard body you're listening to.

In general parlance, "Serial", without additional specifiers is generally assumed to mean asynchronous serial with data patterning following the RS-232 standards, though the signaling levels can vary (generally either TTL or -12V - +12V).

Saying something goes through the UART tells you nothing, unless a specific UART on a specific chip is specified. There are UARTs out there that do all sorts of interesting, non-traditional-serial protocols.   



Saying "UART Communications" is similar to saying "Vehicle Travel". Most people would probably think of a Car, until one guy shows up in a plane, the next guy a boat, and one random wacko in a giant hamster ball. They're all still vehicles, and as such all technically correct. 

You should never make assumptions like that unless you know the person who says "UART" well enough to feel confident [s]he means what you think [s]he means.