An RSS feed is a publication that you can subscribe to without needing to give any personal information, such as your email address.
Website would publish their blog entries to an RSS feed so you didn’t need to keep going to their website, or give your email address to get it sent to you that way.
A "raw" RSS feeder will fetch the RSS entries and display them for you.
I presume paid features are meta around the RSS feeds.
So you could add your own notes to the items.
You could have groups/categories of items beyond just grouping by their source.
The service might fetch/cache them automatically, whereas a free one might not have an "always on" type functionality and might miss posts if it's not pulling ever month or whatever (same, with errors).
On top of that, if another user on the service is subscribed to an RSS feed, you might be able to access the feeds history (beyond the timescale/history the feed keeps published).
The service might be able to highlight and alert you to updated posts, showing the difference between the revisions.
The service might also be able to recommend similar RSS feeds based on other users interests, aiding in discovery.
And all of this would by automatically synchronised between devices.
There is a difference between every reader. You should try a few and find out which one works well for you.
But yes, there is no fundamental difference between free and paid. For hosted readers free will often have tighter limits on the number of feeds you can follow and how often they update. They may also provide add-on features such as summarization and automatic organization. For local readers paid readers may just have features disabled until you pay.
Windows (cross-platform): GitHub I’m not listing links for all 6-ish platforms of just this one individually just go here.
The aforementioned are readers which can either read feeds saved in them locally, or on a supported service. If you wish to self-host a feed aggregator (so you can sync your read articles etc across platforms), I recommend FreshRSS.
NetNewsWire can sync this stuff over iCloud.