Star Trek Social Club

The Technical Manual explanation is not that replicators create matter out of pure energy - they are a type of transporter that dematerializes raw material and rematerializes it to match a molecular pattern. They are "matter-energy converters" only in the sense that the stream of particles during the materialization process could be called an energy stream.

These replicator system headends are located on Deck 12 in the Saucer Module [of the Enterprise-D] and on Deck 34 in the Engineering Section. These systems operate by using a phase-transition coil chamber in which a measured quantity of raw material is dematerialized in a manner similar to that of a standard transporter.

Instead of using a molecular imaging scanner to determine the patterns of the raw stock, however, a quantum geometry transformational matrix field is used to modify the matter stream to conform to a digitally stored molecular pattern matrix. The matter stream is then routed through a network of waveguide conduits that direct the signal to a replicator terminal at which the desired article is materialized within another phase transition chamber.

IIRC there are 3 different methods seen for food creation in Star Trek.

Protein Resequencers (ST:ENT, ST:TOS): which presumably take stored amino acids and combined them with supplementary minerals and flavouring into nutritious cubes that look like marshmallows.

Matter Recombinators/Food Sythesizers (ST:TOS): capable of taking stored matter and producing 'simple' foodstuffs like drinks, iced cream, slabs of protein similar to chicken breast or steak, etc. I think these were sometimes called replicators but the distinction is the production is done elsewhere and the food delivered in seconds on request.

Replicators (ST:TNG +): I swear they described this as direct energy to matter conversion but I can't find the source for this. The seemingly ridiculous energy demands this requires can be justified by the fact they use matter+antimatter reactions for energy supply. A cup of water would take a cup of fuel give or take. (edit: To confuse the issue, it's also described in Discovery that waste matter is broken down and used for things like replication, but matter=energy so it is all the same in the end).

Transporters: it's been clear from the beginning the matter is being deconstructed into energy and sent to the destination where it is reconstructed using the original's pattern. The ethics of it are dubious because every time you see someone transport they are being literally killed in front of your eyes and a new copy created elsewhere.

Admiral Vance:

"It's made of our shit, you know?"

The replicators work very well, thank you.