Please advise on this conversation we had over on c/Piracy. Transporters and replicators, basic operating principles?

Well, as noted in that conversation, it wouldn't work in the real world.

My understanding of canon is that transporter technology does use the energy produced by the warp core to deconstruct matter into energy, then reconstruct it at the desired location.

In that process, a computer has to hold the "pattern" long enough to make the transition possible. Hence pattern buffers.

Replicators use the same method, but have what amounts to better memory, and lower resolution.

A transporter can reconstruct things to such a small scale that every synaptic connection remains intact. Replicators can't. They are, barring some exceptions that don't really make sense, unable to produce anything alive.

A replicator cab only produce something it has a "recipe" for. At some point, someone used a transporter or similar device to deconstruct a given thing, like a hot cup of tea. That "pattern", rather than being held in volatile memory, was recorded. Iirc, in the novels it was Spock that helped refine the technology to be as useful as it would be in TNG, but I haven't read those in ages.

So, when Picard wants "earl grey, hot", the replicator pulls up the pattern, uses the energy from a source that isn't well specified, and turns that energy into matter. Literally every single cup of that tea is going to be the same, within the ability of the replicator to resolve. Since tea isn't complicated in terms of long chains of molecules, it should be the exact same cup of tea.

However! There were instances I recall seeing of people adjusting replicator files. Tweaking them to their liking.

And, there's on screen use of big replicators to turn out shuttle parts, as in body pieces.

There's apparently an upper limit on complexity, which was supposedly about not wanting to make things too easy and make it harder on writers to come up with viable plot points. After all, if you can just replicate entire ships, things get crazy fast. "Oh, the Klingons are invading? Let's churn out a few dozen extra battle cruisers"