Other cookies are "persistent cookies", meaning that they survive after your browser is closed. Most persistent cookies are set to automatically expire after a defined duration (for example, a few days, weeks or months). When you return to that website (or visit other websites that use the same cookies) the website provider or its service providers can recognise the persistent cookies they have set and recognise your browsing device.
Local storage: Local storage files are created by apps and websites to store information locally on your device. They are very similar to cookies, but can have slightly different properties (for example, local storage can be used to store more information and can be stored in a different location on your device to cookies). Local storage is normally used to speed up app and site functionality and remember your preferences.