Irish, whenever you use GTAW aka tig, the G in both stands for "gas" which is used to shield the puddle from air. So they all have a gas (argon or whatever gas you use) hookup. What's different is how the gas gets started flowing when you start to weld.
In the most simplest form, you would just use the valve on the gas cylinder. Turn it on by hand before you strike an arc, turn it off after you're done. Gas flows the entire time even though you're not welding. Obviously lots of wasted gas.
The next "step up" is having a valve at the torch. You leave the gas cylinder open the entire time, and control whether gas is flowing with a second valve (in addition to the one at the cylinder) on the torch. Again, manual - you turn it on and off by hand, but you don't have to walk back and forth to the cylinder. The valve is right there in your hand as part of the torch.
Finally, the third way is to have the "valve" inside the machine that is solenoid operated. The torch has no valve. When you "pull the trigger" for an arc, electric current inside the machine causes the solenoid to open the valve. Gas flows. When you break the arc, the solenoid closes the valve. On some machines you can have "pre-flow" and "post-flow" where the gas starts when you pull the trigger but the arc doesn't start immediately, and when you break the arc, gas continues to flow for a few seconds to protect the hot weld and cool it a bit.
If you're going to have a gas solenoid, the machine ought to also allow you to adjust to have pre and post flow, otherwise I don't see an advantage (other than if you have a torch mounted manual valve, you could "forget" to turn it on or off). With a torch mounted, you have the ability to have pre and post flow because you decide when to start and stop gas, before striking the arc and after breaking the arc.
As for HF, there's advantages because it's easy to learn to strike the arc. It just "jumps" on. Disadvantage is if you have a pacemaker or electronics that high frequency current could affect. I'm getting used to lift arc but it took a few attempts to figure out what I'm supposed to do. Only tig I had done was in community college and it was with a miller synchro, water cooled, upslope, downslope, HF the whole shootin match and a comfortable chair and table. Very nice compared to my garage.