There are two bands that go by the name the Psychedelic Furs. The first was a radical and stylish part of the British post-punk second wave; it inspired a legion of followers, paved the way for New Wave, and continues to influence underground rock to this day. The second band known by that name is a different creature entirely: a fewhit, synth-pop wonder, it has been rightfully consigned to the dustbin culture of “I Love the 80s” nostalgia along with “Pretty in Pink,” Molly Ringwald, and blow-dryer bands. Both will be performing tonight at the Supper Club.

Though they broke up in 1991, the Psychedelic Furs are still relevant today. One reason is that they reunited in 2000, and have been playing sporadically ever since; the second, and better, reason is that they are routinely cited among the influences of modern retrorockers like the Killers, Interpol, and the Rapture. What people fail to realize is that the Psychedelic Furs were themselves a retro-rock band in their day.

The Furs emerged out of the musical flux and flummox that followed English punk rock in the late 1970s. In the beginning, they wore their influences prominently and proudly on their sleeves: David Bowie, Johnny Rotten, the Velvet Underground – especially the Velvet Underground. It seemed everything about them was a tribute of some kind. Their name was a nod to a Velvet Underground song (“Venus in Furs”), and their buzzed about live shows recreated elements of Warhol’s Exploding Plastic Inevitable, down to the Lou Reed sunglasses and whirling projections.

Richard Butler’s scratchy monotone would become one of the most distinctive voices in pop music, but on the group’s self-titled 1980 debut, you can hear him shopping for a sound. Jonathan Richman’s sleepy sneer (“We Love You”), David Bowie’s aloof nasality (“Sister Europe”), and Johnny Rotten’s mocking bark (“Pulse”) all get trial runs on the record.

He may not have found his voice yet, but he knew what he wanted to say. Butler had already settled, by then, on the abstract, snatched-scraps approach to lyrics that would define his songwriting style. He sings on “Flowers”: “In the eastern carpet store / he is made of dreams / put his picture on the wall / just where the mirror gleams / his body is upon the wall / his teeth are sharp and white / we cut his face with razorblades / and out of him comes foul white light.”

To call the Furs’ sound derivative is accurate, but unfair: Drawing upon the past, they managed to derive something new. They called their sound “beautiful chaos,” and the description is apt. Their first record combined swirling guitars, saxophone, throbbing bass, and punkish attitude. It captured the intensity of the band’s live set, and today seems both backward and forward looking. It recalled a Velvet Underground jam, and anticipated shoegazer rock, a style that wouldn’t even earn a name for almost a decade.

What it didn’t anticipate is the synthpop band that the Psychedelic Furs would become. That trajectory was clearer by 1983’s “Forever Now.” The Furs had begun to register with fans in England and, to a lesser extent, the United States, and they entered the studio for “Forever Now” with the goal of crafting a poppier sound and reaching a larger audience. Picking up on what Soft Cell and others were doing, they decided synthesizers were the means to accomplish it.

They were right. With its tinker-toy marimba and brush-stroke synth, the first single from the album, “Love My Way,” became a breakout hit. It established the Furs as early stars of MTV and propelled the album to gold status in the States.

It also determined the band’s future; from there, they marched steadily toward the mainstream. “Mirror Moves,” their next album, contained a couple progressive synth hits: “The Ghost in You” and “Heaven.” But it was a rerecorded version of “Pretty in Pink” (originally issued on the 1982 album “Talk Talk Talk”) and the John Hughes film that took its name from the song that would truly change their fortunes – for better and worse.

The movie was a blockbuster and instant generational milestone. Many of the bands featured on the soundtrack – Suzanne Vega, Echo & The Bunnymen, OMD – benefited from the increased exposure, but none so much as the Furs. Hot on the heels of “Pretty in Pink,” their 1987 album “Midnight to Midnight” became the band’s most successful to date, reaching no. 12 on the Billboard charts.

It is also generally acknowledged – even by the band – as their worst, and the beginning of the end. The video for “Heartbreak Beat,” the album’s lone hit, finds the Furs transmogrified by pop. Once the image of understated cool, Butler here looks like the unholy offspring of Billy Idol and Duran Duran (fey biker leather, lots of mousse). The Furs would limp through two disappointing albums before finally calling it quits.

Which brings us back to the present. It’s one of the advantages of reunion that a band can step outside its timeline and escape the corners it painted itself into. There are few groups for which this matters as much as for the Psychedelic Furs. With this working for them, tonight’s show ought to make for an entertaining – if mismatched – double bill.

The Psychedelic Furs will play at the Supper Club tonight at 7 p.m. (240 W. 47th Street, between Broadway and Eighth Avenue, 212-921-1940).