Listing types allow you to separate different types of content that you will be listing on your site e.g Places, Events, Real Estate, Cars etc.
You plan to list properties for rent and events in your site. Properties for rent may require a field named "Number of rooms", while events may require a field "Start date". In this case, you have two different types of content which have fields that make sense for one kind, but not for the other.
This is a great example when you should create two different listing types, Events and Properties for rent, so you can organize your content and create a better experience for yourself and your users
While we explained above what listing types can do, categories on the other hand are just a field, a simple filter which can be used to filter listings of a specific listing type. They don't have any other purpose or feature other then filtering your content.
Each of these listing types have their own filters, fields, preview card, single page.