Yep, to my knowledge you need a monitor with GPS to track mileage (such as a Garmin) which comes with a chest strap.
The monitors that don’t have chest straps have “pulse sensors” on the face of the watch. It doesn’t keep a continuous heartrate like the ones with chest straps so you only get readout when you press the sensors down with your fingers. It’s basically taking your pulse and not tracking your heartrate.
I have both types. I bought the Reebok S6 (I believe that’s the model number) that has the pulse sensors and not the strap. I used it for 2 years and it was great for a stopwatch and to get a quick readout of my heartrate at that moment.
I just got a Polar F11 for my birthday and I LOVE it! It comes with the soft wearlink chest strap that you don’t even notice when it’s on. I hate that constricted feeling too, but this is very comfortable. Anyway, this thing is amazing! It tracks everything and has some very cool features.
Kathy