Here’s what Memory Alpha says about holomatter:

Holodeck matter, also known as holomatter, was a partially stable substance giving the illusion of solid matter, held together by force fields created by hologenerators.

Outside of the range of holographic projectors this substance lost cohesion and quickly dissipated into energy. Within range, this substance could have all the properties of "real" matter but was controllable by complex computer software.

We’re also told in the TNG Tech Manual (which I assume started as the actual writers bible for technobabble, then got prettied up for publication) that the holodeck uses a combination of 3D directed sound and light projection for those two senses, with force fields to simulate the touch of walls, immovable objects, and treadmill-like floors. For objects which can be picked up or are intended to be tasted, replicators quickly create props of sufficient fidelity from the ship’s object store archives.

(I postulate there are also aerosol sprays to simulate scents, to enhance the realism of each scene. When a holodeck scene shuts off or turns on, ventilation fans quickly move scented air out of or into the holodeck, causing a whooshing noise. Invisible air-channelling force fields are why the users don’t notice the air being quickly replaced, why their hair doesn’t shake in the violent wind. This is the main reason there are bio-matter filters; they clean the scent additive chemicals from the air, along with any dust, moisture, skin, pollen, or other contaminants.)

Usually, “force fields” hold things and “tractor beams” move things around. But what if the “force” of the holomatter “fields” is something completely different than the usual barriers or tractor beams we’re familiar with?

I assume that replicators and transporters both use waveform-collapse technology to materialize objects, as u/Safebox explained in the waveform transporters, not quantum teleporters post. Transporters use a high-fidelity pattern scan and the original matter, while replicators use a synthesized or scanned waveform pattern and source their matter from a waste-matter slurry.

I theorize that holodecks use something very similar to a transporter/replicator waveform pattern materializer. However, instead of a matter stream, holoprojectors project a resonating low-energy force field into the universal ambient field of virtual particles which already exists everywhere, which perturbs the field and allows the holo-replicator to collapse quasiparticle waveforms into macroscopic virtual matter: holomatter.

Holomatter can only exist within the low-energy fields emitted by the holoprojectors, by the Doctor’s holo-emitter, or by a holo-communicator ring. Once materialized by a holo-replicator, it exists as long as it’s within that low-energy field.

Holomatter interacts normally with electromagnetism and with gravity, which is why light bounces off holocommunications based on the lighting where the projection appears instead of the source location. It’s also why people can touch holomatter flesh in holosuites, and baseball can be played with real-world physics.

Although most distant characters in a holodeck are just 3D light and sound projections, holomatter flesh puppets simulate any people or animals within reach of users, or any which are meant to be touched in a given simulation, such as in a holosuite. These puppets are 3D meat with working muscles, constantly moved by the computer like a perfectly-played game of QWOP. This is why they’re usable for Worf’s workouts, and Quark’s customers. However, the computer can still use force fields/tractor beams to directly determine their movement to keep it from being uncanny. This is why the gangsters Redblock and Leech dissipate into the ambient virtual particle field without falling to the ground in “The Big Goodbye”.

Holocommunication rings only create the surface layer of holomatter, which is why they appear ghostly: they’re thinner than paper, lighter than foam, and a bit unsettling to see, especially if they glitch.

This common technological foundation between transporter, replicator, and holodeck, differing mostly in fidelity and matter source, is why Moriarty thought there was a possibility of his escaping the ephemeral existence of a hologram. Data and Barclay attempted to use pattern enhancers to beam a holomatter chair (not a replicated prop chair) off the holodeck.

If Moriarty were just 3D CGI trickery, it would be obviously impossible, but there’s a chance if he was a holomatter flesh puppet being run by a sentient simulation. However, they’d also have to replicate a perfectly functional human nervous system and brain, inside a human body with functional DNA, with the high fidelity of a DNA-safe transporter and somehow transfer Program Moriarty’s consciousness from the holographic mind simulation to a brand-new brain. Worf’s replicated spine and Neelix’ holo-lungs were not nearly as complex as a full body for Moriarty would have been.