Mostly, you can't have different profiles in the tabs of the same window in Chrome, and you can have different containers in the tabs of the same window in Firefox.
E.g. you can run your email tab in the default container, and a bank app in a separate "money" container next to it.
Or you can run one gmail (or outlook, etc) account in one tab, and an another gmail (or outlook, etc) account in another tab next to it.
Also if you only want to separate (log-in) cookies, local storage and that kind of things for certain sites, but don't want separate history, bookmarks, settings, add-ons, etc., which is what you'd also get if using completely separate profiles.
E.g. you can run your email tab in the default container, and a bank app in a separate "money" container next to it.
Or you can run one gmail (or outlook, etc) account in one tab, and an another gmail (or outlook, etc) account in another tab next to it.