Should a brand feel the same everywhere, or is some variation a good thing?

A brand can look great on Instagram and then feel completely different on its website, packaging, or physical space. Not necessarily bad sometimes the format needs its own treatment. But when the differences get too big, it becomes difficult to tell if you're even looking at the same brand. I think there's an interesting balance between keeping things recognizable and giving each platform enough freedom to work properly. Where do you think that balance should be?