ONT stands for Optical Network Terminal of Modem and ONT
The ONT (also called the modem) connects to the Termination Point (TP) with an optical fibre cable. It connects to your router via a LAN / ethernet cable and translates light signals from the fibre optic line from your TP into electronic signals that your router can read.
Modem is short for MOdulator/DEModulator and is only used for three device classes: telephone modems, DSL modems, and cable modems (thx Cody). These modulate digital data on to voice-grade phone lines or (possibly former) television cable. DSL and cable “modems” often include a router, but technically these are routers that include a modem.
An ONT is an Optical Network Terminator, it connects the ISP’s (passive) optical network with your LAN. Normally, it includes a router as well but in theory it could just be media converter.
Optical networks work by sending light pulses over optical fiber, so you actually could argue that they use amplitude modulation of the used wavelength. Accordingly, calling an ONT “modem” isn’t completely wrong from the physics POV but in a networking context, that term isn’t used by people in the know.
The rule of thumb is that “modem” is only used for devices coding digital data onto an “analog” medium – in the sense of its normal or traditional use. Of course, technically all media are actually analog in their physical nature