These two terms get used interchangeably so often that most people assume they're the same job. They're not, and mixing them up is how companies end up paying for a logo when what they actually needed was a decision.
Brand strategy decides what a brand should stand for and to whom. Brand identity is the visual system that makes that decision recognisable: the logo, the colours, the type, the way a photo gets cropped. Strategy is the argument. Identity is how the argument looks.
Identity built before strategy tends to be pretty and forgettable, because there's no underlying decision for the visuals to express. It can still look professional. It just won't hold up under pressure, the first time a new product line or a new market doesn't fit the aesthetic that got chosen on a whim.
If your team can't agree on what the brand stands for without a meeting, that's a strategy gap. If the strategy is clear but every asset still looks like it came from a different company, that's an identity gap.
The best identity systems are just strategy translated into something you can see. A distinct point of view and a distinct look, built in that order, reinforce each other. Built out of order, they usually just coexist.