The distinction isn't just "mobile". Each mobile device a person uses has a separate secret chat, not synchronised with their other devices.
There's someone I talk with on Telegram where we have two secret chats open all the time, one for their iPhone and one for their iPad. Both channels are connected to my phone.
I have to guess which chat to write in for the other person to notice that I'm writing to them...
That's because when using their iPad they often don't have the iPhone nearby (no need for most purposes). It's lucky I don't have two mobile devices too, as then we would have four secret chats.
When I'm at my computer, we can only use the non-secret Telegram chat, which has a nice GUI but unlike my phone cannot connect to either of the secret chats. This isn't really a problem because we use the non-secret chat for most topics anyway, because of the search and synchronisation.
(Aside, the ability for the other party to delete old messages in Telegram is not very cool imho. I know someone who fell out with a friend and their friend deleted their entire multi-year conversation history, which was heartbreaking. Once you have a long history of messages with someone I think it should be part of your personal archive to look back on. It feels permanent until that point, so it's a surprise to find it can all disappear.)