MuseScore native format (*.mscz and *.mscx) are backward compatible: MuseScore 4 opens MuseScore 3's *.mscz without error.
MuseScore native format has never been forward compatible, see forum discussion. Although partial data retrieval is still possible as of MuseScore 4.0.2, you should not rely on it for score data integrity. Some features present in MuseScore 3 have not (yet) been included in MuseScore 4, and internal data conversion occurs when you open a older version file with a newer version program and then overwrite the file using the save function.
Some users find it useful to keep all data intact by creating seperate folders to store score files designated for editing on different Musescore versions, it is recommended to duplicate files before opening them as required.
In the File menu you can find options for opening, saving, exporting and printing your file:
To open any supported file:
Open recent allows you to choose from a list of recently-opened scores.
Save, Save As…, Save a Copy… and Save Selection… allow you to save native MuseScore files (.mscz and .mscx).
Export... allows you to create non-MuseScore files, such as PDF, MusicXML, MIDI, and various audio and image formats. In the Export dialog, you can choose which format to export to.
MuseScore remembers which format you picked the last time and makes that the default for the next time.
Print... allows to print your MuseScore file directly to a printer from MuseScore. Depending on your printer you will have different options, but generally you can define the page range, number of copies and collation.
If you have a PDF printer installed, you could also "export" to PDF using Print, but it's usually better to use the native PDF option under Export for more accurate rendition. Note: For this to work properly with Adobe PDF, make sure to uncheck "Rely on system fonts only, do not use document fonts" in Printer properties.