The primary difference between the Schema Markup Validator and the Rich Results Test from Google is that the Rich Result test is restricted to testing only the markup of structured data that's used in Google's results for the search. However, the Schema.org markup validation is more intended for "general purposes" and is geared towards debugging various other types of structured data in addition to the ones that Google supports.
Currently Google supports only a limited number of Schema Markups that includes:
Article, Breadcrumb, Carousel, Course, COVID-19 Announcements, Dataset, Employer, Aggregate Rating, Estimated Salary, Event, Fast Check, FAQ, Home Activities, How-To, Image License, Job Posting, Job Training, Local Business, Logo, Math Solvers, Movie, Practice Problems, Product, Q&A, Recipe, Review Snippet, Sitelinks, Search Box, Software App, Speakable, Video, Subscription and Paywalled Content, Article / Blog Posting, etc.
This means that the markup validator may be showing that there are no issues with the way your schema is written syntactically, but Google may still have an issue generating a particular type of search result based on that schema.
Both of the tools can still be used for better SEO and achieving featured results in the SERPs. The Rich Result Testing tool doesn’t offer the code editing option though, so the Schema Markup Validator tool can come in handy for troubleshooting any Schema markup issues.
There are a number of Data Types supported by the Google Rich Result Testing Tool for existing Schema Libraries supported by Google and those Data Types can be used when testing different types of the Schema markup through Schema Markup validator tool.