Everything your post mentions is a signalling protocol, some higher-level than others.(AHCI & NVMe run on top of SATA and/or PCI-E, for example.)
Form factor: Let's go back in time to the DIN-5.
Five wires. Depending on which pin had which voltages/signalling, and what it was plugged into, the same "connector" was used for all sorts of different
protocols - everything from MIDI interfaces, to composite video output (TI-99/4A personal computers), to floppy drives, to keyboards.
That's form factor.
The protocol, however, varied. (That's which pins do what, at what voltages, and how that's interpreted by the computer/device on the end of the cable.) Which is why I couldn't plug a MIDI interface into my TI-99 and hear PacMan or something. The two devices didn't have a protocol in common to speak to each other.
An interface is... probably best thought of as another word for the protocol. (SATA and microSATA are different physically, but they're easy to wire to each other; it would be silly to think of them as different interfaces. Same for most USB varieties.) It's usually pretty easy to adapt one physical form factor to another if the protocols are the same (or similar).
Nowadays, the form-factors don't often get recycled for multiple protocols, so you don't really have to worry about the difference. Connector, protocol, interface, etc., are all basically the same thing now.
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