Jason Bulmahn also ran a game for Geek & Sundry that used theatre of the mind.
As for the differences, I think Draw Steel looks much more immediate in what it does – particularly for what passes for martial characters. In PF2, the stuff martial characters do tend to be based on normal maneuvers that anyone can do (though of course training and skill feats and such helps).
For a low-level example: PF2 has the action Shove, which is a thing anyone can do using the Athletics skill vs the opponent's Fortitude DC. On a success, the opponent gets pushed 5 ft away, and you can follow them but doing so provokes an opportunity attack from anyone else. Fighters can learn the Brutish Shove feat, which gives them the benefit that if they're using a two-handed weapon and are making an attack with a multi-attack penalty (the Press trait), they can also Shove the opponent on a hit (without an additional roll), and follow up without triggering OAs. There are also upgrades you can take at level 4 and 12. The only limit to how often you can use this is that you need to have made an attack already on your turn, so the combination costs 2 of your 3 actions.
The closest equivalent in DS would be the Fury ability Brutal Slam. You just make a power (attack) roll, deal damage, and push the target 1/2/4 squares depending on the roll. No muss, no fuss. There's also a Fury ability named "Out of the way!". Depending on your roll, you hit for 3/5/8+Might damage and slide the target 2/3/5 squares. BAM! Done. Much more significant effect, and you don't have to jump through hoops. Much like in PF2 you can follow along, but doing so doesn't protect you from the equivalent of OAs, but any such damage you take will also hit the target. However, this ability does have a low-ish Ferocity cost, so you can't spam it like you in theory can with Brutish Shove.