A Custom App is a Lightning navigation grouping — the dropdown at the top-left that organises a set of tabs into a coherent workspace. You create one in Setup -> App Manager -> New Lightning App, choose Standard or Console navigation, assign tabs, and grant access via profiles or permission sets.
Apps don't grant data access — they just present a curated set of tabs. Same Account record looks different inside a Sales App vs a Service App because the surrounding context (related tabs, layout, utility bar) differs.
A Connected App is something else entirely: it's an OAuth integration registration. When an external system (Mulesoft, a mobile app, a script) needs to authenticate to Salesforce via OAuth, it does so as a Connected App — a record that defines the consumer key/secret, callback URL, scopes, and IP relaxation rules. Connected Apps live in Setup -> App Manager too, which is where the naming confusion comes from.
Rule of thumb: if it has tabs, it's a Custom App. If it has a consumer key, it's a Connected App.