Each remaster and remake has to be taken on its own merits. There isn't a set procedure.
Metal Gear Solid Delta is perhaps the most faithful because it doesn't remake everything. Using the original VA for 99% of it ensures that it stays tethered to its roots, and if it didn't have technical/performance issues I'm sure it would have been universally praised.
Spyro Reignited was also very faithful, pretty much just making gameplay consistent across the trilogy.
Resident Evil's first remake was mostly faithful but added gameplay sections and changed the tone.
Resident Evil's 2, 3, and 4 remakes are all reimaginings of various degrees, with 3 being so unfaithful that I think the reaction influenced 4R's development.
The same can be said for remasters.
Legacy of Kain: Soul Reaver 1+2 Remasters are very well done from what I can tell).
Bioshock Remaster had mixed reviews because the remastered graphics arguably detracted in certain spots, but it did add things like developer commentary, a WIP museum, and NG+.
Dark Souls Remaster was largely pointless for anyone on PC because it was less a remaster and more a tweaked settings port, and 10 years before it wouldn't have had that label on the box and would have been described as an enhanced port.