Ok, I did a change in one of my SPFx web parts, incremented the version in package-solution.json file and deployed the app in the app catalog.
In the Dev site I went into the Details for the app, and I saw the new version there and clicked in the Get It button.
I went in the page where the web part is and refreshed the page and it was updated successfully.
However, for my surprise, I went in the production site (in the same tenant) and refreshed the page and the changes were there as well! It was strange because I didn’t go to the Details and clicked in the Get it button in the production site.
How can I have different versions of the same web part in Dev/Stg/Prod?