Why do I have to change Media Sets to create a Full Backup to a new file and what does that mean?
It's quite a long topic and for the most part it relates to technology that is irrelevant in this day and age (more specifically: tape storage). However here is a quick summary:

media set
An ordered collection of backup media, tapes or disk files, to which one or more backup operations have written using a fixed type and number of backup devices.
media family
Backups created on a single nonmirrored device or a set of mirrored devices in a media set
backup set
The backup content that is added to a media set by a successful backup operation.

In short, if you create a new media set on a device, then yes, you will lose all of your previous backups:

Creating a new media set
To create a new media set, you must format the backup media (one or more tapes or disk files). The formatting process changes the backup media as follows:

Deletes the old header (if any), effectively deleting the previous contents of the backup media.

Formatting a tape device deletes all previous contents of the currently mounted tape. Formatting a disk affects only the file that you specify for the backup operation

Writes a new media header on the backup media (tape or disk file) on each of the backup devices.



For more information, checkout the Media sets, media families &amp; backup sets documentation over at Microsoft Docs.