same address on our email list twice, once with capital letters

technically the part before the @ can be case sensitive by the spec, but none of the big mail providers do that, so merging is safe. if your email tool has a setting to lowercase or dedupe on import, switch it on and this stops happening.

Same inbox. Mail providers don't treat capitals differently, so merge them. Before you delete one, check whether either copy is unsubscribed. If one is, keep the unsubscribe, otherwise you're mailing someone who opted out. Then lowercase emails in whatever form or import created the duplicate. It's usually an integration or a CSV upload that skipped the normal dedupe.