Web vs. Mobil Development: data storage

Curious is it possible to store data / records in web development permanently in browser?

I am developing native apps for iOS, and want to understand how web / javascript works.

Usually when app in native development is downloaded first from App Store and first it is launched, client fetches a lot of data from server, and afterwards at next launches when app is running only record changes moves back and forth. Is it possible these kind of data transfers in web development?

In iOS development Core Data is kind a of a ORM local database, on which JOIN operations can be performed. Is it any local database on web development that provide JOIN like operation?