I assume you want:

• a persistent Linux USB stick (basically you can take your OS and your files with you on the go, and everything is stored on the USB), and
• a Linux install on a desktop/laptop, which you created using your persistent USB from above.

I believe this is possible by just creating a Live USB stick with a persistent partition, you can store files on the persistent partition, and still have all of the installation tools you usually find in a Live USB. On Windows, this can be done with Rufus. Or you could use Ventoy as described in this guide.