Whitening works by getting peroxide onto the tooth and keeping it there. Everything else is a delivery mechanism, and most of the mechanisms sold over the counter are poor ones.
Charcoal pastes are abrasive. They scrub surface stain and, used often, thin the enamel underneath — which makes teeth look more yellow over time, because the dentine beneath enamel is yellow.
Custom trays work because they hold the gel against the tooth and off the gum for hours at a time. That is the whole trick, and it is why a fitted tray beats a one-size strip.
One thing worth knowing before you start: crowns, veneers and white fillings do not change colour. If you have any at the front, whitening the teeth around them changes how well they match.