Studio 5000 is RSLogix 5000. They are the same program. It just changed names after version 20. And yes, version 20.04 clears up the issues between 20.01 and 20.03. So everything up to version 20 = RSLogix 5000. Everything from version 21 up = Studio 5000. The only difference is that starting in version 27, Studio 5000 included the View Designer which is for the new Panelview 5500 terminals. One day, the Panelview 5500s will be worth buying, but not for a while.
Also, keep in mind that there are processors starting to come out that will not work with RSLogix version 20. The new Control Logix 5580 processors require a minimum of version 28. If you get newer processors in the future, your copy of RSLogix might not work with them.