I speak AmE, mostly informally; and I have broiled any number of steaks in the past. I like my steak broiled, and I hope to broil many more steaks in the future. I wish I were broiling a steak right now, or that I had finished my cooking and were sitting down to eat my freshly broiled steak.
I usually broil my steaks by laying the steak on a grill over an open fire or under a gas flame or electric heating element.
I could also skewer the meat on a thin (1/8" or so) metal rod 18"-36" in length, and then hold one end of the skewer in my hand and use the other end to hold the meat over a fire (or other heat source) until it was cooked to my satisfaction. ("Skewer" is both the noun for the metal rod, and the verb for getting the food in place on that rod.)
If I got tired of holding and turning the skewer over the fire, I might wish I had a spit over the fireplace: a metal rod at least 1/4" or so in diameter and a couple of feet long, resting in two forked rods standing vertically on either side of the fire, with a handle projecting from one end of the spit. Then once I got my steak spitted onto the rod, I could turn my steak over the fire simple by turning the spit handle. (Once on the rod, the meat has been "spitted" there; but I've never heard anybody use "spit" as the verb for doing this in the present tense. I think I would have to place, put, thread or even skewer the meat onto the spit; or impale the meat with the spit; in order to get it spitted and ready to broil.)
If I used a grill, I would call mine a grilled steak, or a broiled one.
If I used a skewer, I would call my steak broiled or roasted.
If I used a spit, I would call it a roasted steak.
I would not call it a barbequed steak unless I had applied a barbeque-type sauce to it during cooking, even though I might have used a barbeque grill to cook my broiled steak. (However, I have only ever lived along the West coast of the US. For serious BBQ and serious BBQers & BBQ terminology, you'll need someone from the southeastern US.)