Even leaving aside its origins as prison slang, punk has always meant different things on either side of the Atlantic. Forty-five years ago, in New York, no punk band sounded like the next one: the only thing that linked Ramones, Talking Heads, Patti Smith, Suicide, Blondie and Television was that they played the same club, CBGB. Over here, by contrast, punk was rapidly codified into people shouting angrily over buzzsaw guitars. These days, it can seem as though the opposite applies. It’s the American punks who stick to a formula, while in the British Isles, the punk label seems to apply to any band with a guitar and a modicum of attitude.

Both Turnstile (from Baltimore) and Fontaines D.C. (Dublin) have been called punk. And they have about as much in common as trifle and shepherd’s pie: from a distance they might look roughly similar, but up close there’s nothing to tie them together. Turnstile are one of those bands for whom precision and discipline are everything — they put one in mind of those stories about Black Flag in early-1980s Los Angeles, rehearsing for hours on end every day regardless of whether they had any gigs coming up. Fontaines D.C., by contrast, are slovenly (not sloppy; their rhythm section is electrifying), and have a very distinct air of being too cool to care hanging over them.

Turnstile have come through the American hardcore punk scene, hardcore being a genre built on velocity and rage, but they’ve became rather more than yet another band of lightspeed thrashers. Their third album, Glow On, was one of the triumphs of last year, attracting attention from outside the insular hardcore scene, and propelling them to two big and rammed London shows. It had all the energy and aggression of hardcore, but with extra invention and melody.

Their show in Kentish Town was simply one of the most exciting hours I’ve spent in ages, which was curious in itself given how much there is about Turnstile I would normally hate: proximity to rap metal; sportswear on stage; half-speed breakdowns, where everyone does that headbanging from the waist thing; the singer having his own little kit to do extra percussion on (no song, ever, has been improved by a singer tapping away at a couple of little drums. That’s just science. I’m pretty sure Sage would back me up on it).

It certainly helped that the singer —Brendan Yates — was absolutely magnetic. He certainly fits the muscular template of hardcore punk, as he was keen for everyone to see once he took his top off. But he was no musclebound lunkhead: he was more like a ballet dancer or an ice skater (at one point he did what I think was a double Salchow across the stage). He spent as much time performing genuinely elegant leaps and bounds, his hips swivelling with every step. It was an unexpected complement to the force of the music.

And how forceful that music was: precise, hectic and thrilling. At their best — and most ambitious — Turnstile sound like they are trying to remake ‘Kashmir’ by Led Zeppelin as a 150-second song. They crammed 24 songs into an hour, as if trying to break the land-speed record, but the precision meant every chord change hit the target, no matter the speed. I should say that if you have no taste for hardcore’s machine-gun attack, Turnstile will not be for you. The friend who came with me left after 20 minutes, but I like to think he was the only QC at the Commercial Bar who went to see a hardcore band last week.

On paper, Fontaines D.C. are much more up my street. On stage they weren’t. One problem is their second album, A Hero’s Death, which got rave reviews but to me sounded very much like a victim of second-album syndrome. I’d bet a tenner that most of it was written on the road, because it sounds to me like a record where no one was really thinking about songwriting so much as finding grooves and then finding things to go on top of them. I don’t think it was coincidence that the two most thrilling moments in their set at the Dome — a small show to raise money for War Child; they can headline Ally Pally — were two songs from their first album. ‘Hurricane Laughter’ was all feverish intensity, ‘Boys in the Better Land’ has a simple chorus hook so carefully deployed it hit much harder than it had any right to.

It’s not that Fontaines D.C. aren’t good. They plainly are. I like them plenty. But there was a stark contrast on consecutive nights between a group playing with the complete conviction that the hour they are on stage is the most important hour of their life so far, and one radiating an air of doing the audience a favour. I’ll happily go to see Fontaines D.C. again, but I’ll run to see Turnstile.