Whenever Word documents are imported into Writer, all the MS Word fonts used will be converted to its equivalent web fonts in Writer.
Exporting with MS Fonts
When such imported MS word documents in Writer are then exported, the equivalent web fonts that were first used instead of the MS fonts, will be automatically replaced with the the original MS Word font upon export and hence the font family will remain uniform.
Exporting with Bundled web fonts
In case of exporting a document that's created in Writer into docx format, then the web fonts used in Writer will be bundled to the exported Word document.
However, this rendering font behaviour purely depends on the version of MS Word being used and differs based on the type of platform used like Windows or Mac.
In a Windows machine, Word will consider the bundled web fonts at first glance. However if the Word document is saved again as a new document, then MS Word will automatically remove these bundled fonts.
In case of Mac, MS Word considers embedded fonts only for Office 365 Subscribers and Office 2019, where the version should be greater than 16.17. With such varying differences in rendering fonts in Word, import/export font behaviours like this purely depends on how MS Word works.
Bundling new fonts in Word
Writer provides a convenient way to use system fonts via Custom Font mapping in case you want to bundle your own fonts in MS Word and use the same in Writer as well. However, the same doesn't hold true for Word.
For instance, say the user installs a new font named Knockout Font and then uses the same in Writer. Although the font family will be preserved in Writer, this exported document in MS Word will be rendered using a fallback font instead of the actual Knockout Font that the user had earlier installed. Again, this varying difference in rendering fonts purely depends on MS Word.
In some cases, users may need to restart the system to allow MS Word to make use of the newly installed font, after which exported docx will be rendered using the newly installed font.