Does the Magsafe charger only charge the iPhone when it’s plugged in?

It's wireless when it comes to the way you charge the iPhone, i.e the connection between the phone and the charger is wireless. Its a magnetic attachment, you don't actually plug anything into the iPhone.

The connection between the charger and the wall outlet is not wireless.

Yes, The MagSafe charger does not itself hold a charge at all. Its not a portable charger. it must be plugged in to power to charge the phone. It is not a battery.

Link-> MagSafe Charger - Apple

Correct. 👍🏼

If you need portability, then I recommend the MagSafe Battery Pack.

There’s nothing misleading about MagSafe wireless charging because you don’t need to physically plug a cable into your iPhone. 