The PS4 also has "applications" plural in it's rest mode message; it's just saying you can have any of your games suspended.
Why would "rest mode" even say that? Unless the PS5 can literally run more than one game at the same time your "rest mode" message wouldn't be suspending plural games.
I don't find the switcher thing all that meaningful either. That term can be used to launch things too particularly with how fast the PS5 can launch games.
edit: To be clear I'm not saying it absolutely DOESNT have such a function, but I really don't think it does.. I believe MS is achieving that by way of using a hypervisor (which they used last gen).. Sony didn't use a hypervisor last gen and really just hasn't discussed anything like quick resume.
Here's the obvious thing in the UI video - watch how they show the sequence:
1. the user is playing Sackboy - the game is running
2. the user joins a multiplayer match in a new game Destruction Allstars from control center - but Sackboy is running.
3. Sackboy was never closed. There is no warning to the user that Sackboy will be closed.
4. On PS4 the user is always warned "your current game will be closed" if you try to boot a 2nd game
5. On the PS5, no warning. This shows clearly the 1st game was not closed, but just suspended.
6. This is not possible on PS4. Multi-game launch/suspend was shown.
They are playing Sackboy and launch another game from control center without any warning of losing progress or game close. This shows the first game is clearly preserved (suspended) not closed, or else the user would be warned.