Hello @JR57, (1) Click the Dropbox icon on the menubar > (2) Click the Account/Profile dropdown menu and (3) check the email address. If it is not the correct address then (4) choose the Preferences... and go to Account tab. There you can Unlink This Dropbox... and then Dropbox will prompt you to login again. Then you can loging using the desired email/dropbox account.
Re: Download Dropbox on MacBook using a different email
One option is manually downloding files and folders from one account and upload to the new account. But if you have lot of data, then it is certainly not the way.
In that case, another option could be (1) login to https://www.dropbox.com/home using your old email, and (2) share the folders with your new account/email.
If you intend to keep your old account, (3) you can just share using email.
If you do not wish to keep your old account, you can go make the account with new account as owner.
Later login using your new account > accept the share > go to folder > again click share button > click the cogwheel/settings button (7) and Unshare folder.
Optionally, you could create sharing links (4) of files and folders from our old account. Copy the links, log out from old account. Login using new email > visit those shared links. Now, on the right upper corner of your browser window you see a Download button, click the drop-down menu and you will find option to Save to my Dropbox.