Metallic dragons have the ability to shapeshift into any humanoid or beast. According to the Monster Manual, it retains many of its stats, including hit points. It also says that "It reverts to its true form if it dies." Does this mean, that unlike with a druid's wild shape, if it drops to 0 hit points while shifted, it dies, instead of reverting to its true form with however many hit points it had pre-shift?
You've already stated the most relevant piece of information in your question: "It retains many of its stats, including hit points".
Direct quote from the MM for good measure:
In a new form, the dragon retains its [...] hit points...
The shortest, most direct answer is that the dragon's shape change ability says nothing about reverting to the hit points it had before the change so it doesn't. When it drops to 0 hit points it just dies (assuming the DM doesn't worry about it making death saving throws).
Unlike the druid's Wild Shape ability, the dragon doesn't assume the hit points of the creature it transforms into. It doesn't gain a separate pool of hit points to its own so there's nothing to 'revert' to. Its hit points (both "current" and "maximum") remain the same in either form so if it drops to 0 HP and dies that means it reverts to its true form and its hit points remain at 0.