When you’re updating Core with the same “minor” version but a different “patch” version – e.g. 7.1.0 to 7.1.3 – all you should need to do is update the Core files and then restart the application (i.e. ?updateapp=<your-app-key> or Update Application from the webtop profile menu).
If you upgrade to a newer “minor” version – e.g. 7.1.0 to 7.2.1 – then you will need to update the Core files, restart the application, and possibly deploy some schema changes. You can do this with ?updateall=<your-app-key> or in the webtop via Admin -> Developer Tools -> COAPI Content Types.