with cookie authentication the user identification is stored in a cookie. it is typically used with browsers as they support setting and sending cookies with requests. if the request requires authentication, (or expired cookie) typically requests redirect to a login page.
with jwt authentication the user identification is passed via the authentication header as a bearer token. browsers do not support using bearer tokens. this method is handy for api's called by application code, because the code can call to get a jwt token to use in subsequent api calls. if the request requires authentication (or expired token), typically a 401 response is returned.
so in general cookie authentication is used with browser requests, and jwttokens is used for api requests.
note: if a browser page has javascript that does an ajax call, because the browser will include any cookies, often cookie authentication is used. care must be taken if the cookie expires because the response is typically login page html. You can add code to detect an ajax request and return 401 instead of the default redirect.