UART Basic Before Writing Code

I have 8051 microcontroller and using Keil, and before jumping into coding, I feel it's better to get a solid understanding of some basic concepts.

I have a couple of questions that I’m a bit confused about:

When we talk about terms like UART, do we refer to it as hardware, software, or protocol? Sometimes I see them used in different ways, and it’s not always clear to me.

To keep it simple, can I refer to it as hardware modules inside the microcontroller? Is that a correct way to think about it?

Also, if UART is considered a software protocol, how can it be full duplex? In code, I usually see we either send or receive a character, not both at exactly the same time. But as per the definition, full duplex should mean sending and receiving can happen simultaneously. Could you please clarify how that works in practice?

I did a little tutorial here.. https://www.electro-tech-online.com/articles/basic-8051-tutorial-5.671/

I use SDCC not Keil but the code is portable by changing the symbols to suit Keil

A UART is a hardware item, nowadays usually a module within an MCU, but originally a separate peripheral device.
(One of the originals is the AY-5-1013: https://rocelec.widen.net/view/pdf/bvesdj0cqf/GSIIS01845-1.pdf )

"Software serial" is an emulation if a UART is not available. And, full duplex in software is possible; it's a lot simpler if the MCU has hardware timers, but possible regardless.