Yes, there are both. Some flow meters (with the ball) can be adjusted but many, like the one you posted, can't. The clear tube with the ball in it has to be vertical or it won't work.
Most of the flow meters that are used for MIG and TIG are compensated fixed pressure, variable aperture devices.
That means that they are set up so:
Bottle --> fixed Regulator --> flow meter --> valve
The flow meter operates at the fixed regulator pressure and that has to be taken into account when the tube is calibrated for flow. This type of flow meter is "compensated" in that there can be some back pressure caused by a kinked lead or a blocked gun and the flow is relatively unaffected.
The 50psi mentioned is the setting of the fixed regulator. When you let go of the trigger, the gas solenoid closed and the gas hose between the flow meter and the solenoid in the welding machine pressurises to 50psi. When you next pull the trigger, that gas releases in a surge until the working pressure drops to around 4 psi.
All I was saying is that if the fixed regulator is set to 20 psi, the surge is much less.
You can, of course, adjust the fixed regulator down to 20 psi. But then the calibration won't be right.
Don't get too hung up with the intricacies of how things work - just pull the trigger and make sparks. Look at the detail if you need to or if you want to.
You can use the same flow meter for MIG and TIG but MIG tends to use more gas. For home use, 25L/m (50cfh) is enough for both.
Jack