UART, RS-232 and RS-485 explained: which one is the protocol and which is the wiring?

UART is the peripheral that produces the framing: a start bit, 5 to 9 data bits, an optional parity bit and one or more stop bits at an agreed baud rate. It says nothing about voltages. Straight out of the microcontroller the signal is at logic level, idle high, 0 V and 3.3 V or 5 V. That is what "TTL serial" means.

RS-232 and RS-485 are electrical standards that can carry that same frame over a cable.

RS-232 is single ended and inverted relative to logic level. A logic 1 is a negative voltage and a logic 0 is a positive voltage, with drivers typically swinging about ±5 V to ±12 V and receivers required to tolerate up to ±25 V. Connecting that directly to a 3.3 V microcontroller pin can destroy the pin, and even if it survives the data is upside down.

A transceiver such as a MAX3232-type part generates the voltages with charge pumps and handles the inversion.

RS-485 is differential: the data is the voltage difference between two wires, A and B, and the receiver only needs about 200 mV of difference to decide. That rejects common-mode noise and allows long cables and many nodes on one pair, which is why drives and industrial sensors use it.

It is normally half duplex, so the firmware must switch the transceiver between transmit and receive with a direction pin and release the bus as soon as the last stop bit has gone out.

A practical way to keep them apart: UART is the framing, RS-232 and RS-485 are the physical layer, and something like Modbus RTU is the protocol on top. For your setup you need three different adapters: the USB-TTL adapter connects directly to the microcontroller pins (TX to RX, RX to TX, common ground, matching logic voltage), the DB9 instrument needs an RS-232 transceiver, and the drive needs an RS-485 transceiver.