The top two in both browsers is what I would expect to see. The volume control missing is expected in the first one due to that window being slightly narrower.
The bottom one for Chrome looks like the standard browser player taking over.
The bottom one for Firefox may well be the same thing. I don't use Firefox so I'm unsure.
I would guess that the issue would be related to the Javascript failing to load. When this happens, you would need to look at your browser console (F12 in your browser and go to the Console tab) and see if there are any errors listed. It may be conflicting with some other code on the page. Also see if the behaviour changes if you switch off any content or ad blockers.