The first is the winsome English rose still best known in Britain for singing a feather-light version of Elton John's Your Song in a John Lewis advert. The second, perhaps less familiar incarnation, is the one America regards - and here she laughs just a little - as an "electronic goddess", primarily thanks to her US No 1 single Lights.
Goulding's most recent recordings do little to clear up the confusion. Those brave enough to venture into the badlands of daytime Radio 1 will be aware of Burn, a ruthlessly catchy slice of Stargate-styled pop candy which recently gave Goulding her first UK No 1.
Those who saw Richard Curtis's new movie About Time will have heard her sing a rendition of The Waterboys' How Long Will I Love You? so delicate it makes her cover of Your Song sound like Napalm Death.
So which one is the real Ellie Goulding? Both, it seems. The 26-year-old from Lyonshall, a small Herefordshire village on the Welsh-English border, insists she has always felt as comfortable with an acoustic guitar as she has soaking up the doof-doof of the dancefloor.
Her parents split up when she was five and her father gradually withdrew from her life, but "back when I still can remember him", she has a vivid recollection of him playing guitar.
Later there was a friend of the family, "an honorary uncle", who was into folk music and played finger-picked guitar. "But then my mum was a massive raver," she says. "She loved dance music, and always played it really loud around the house. Also, we lived in the middle of nowhere, and we were always in the car listening to the radio. So pop music has always been right in the middle of my life."
What holds these two identities together is her utterly distinctive voice: a quavering thing, high yet husky, intimate and emotional. "It is my tool," she smiles, "the thing that connects everything."
Where on earth did it come from? "It definitely took me a while to find my voice," she says, her native Hertfordshire accent smoothed into a classless southern intonation. "For a while I wanted to sound like Imogen Heap, then Kate Rusby, then Bjork. At one point I tired to imitate Beyonce - impossible! So I just ended up with this really bizarre voice. When I listen back to my old songs and demos my voice just goes all over the place. You wouldn't know it was me, whereas now it has all just rolled into one - I can't go back now, I have my own voice and it's quite hard to change. I liked impersonating people, and I think picking up on other singers' inflections and styles has made my voice what it is now."
Goulding says that achieving her first UK No 1 with Burn was "a long time coming". But not really. It's only been three years since she was a much-touted newcomer, winning the BBC Sound of 2010 poll and the Brit Awards' Critics' Choice Award before she had even released a record. Two albums later, and with No 1 singles on both sides of the Atlantic, perhaps it's little wonder that "it all seems like a long time ago".
Starting out her career accompanied by a fanfare of media approval was "a big pressure. If I had known then that I would be here now I wouldn't have worried, but it was a very strange time of ups and downs. It was probably a good thing to be under all that pressure and in the spotlight, because then you have no choice except to go forth! You can't do anything about it. I needed that push, that kick up the a***. I can say that now because I feel confident enough to understand how I got here, not just from all the positive stuff but all the negative stuff as well."
Part of the "negative stuff", presumably, is the tabloid's enduring fascination with her private life. Last year Goulding dated the US dubstep DJ Skrillex, and in the last couple of months alone she has been romantically linked with Niall Horan from One Direction and singer-songwriter Ed Sheeran. I'm left in no doubt from her publicists that this is not a subject that will be up for discussion today. Instead, she is much happier talking about being asked to sing Your Song at the wedding of Prince William and Kate Middleton in 2011. No hint of a rock 'n' roll republican streak here. She jumped at the chance.
"It was one of the coolest things that's ever happened to me," she squeals. "They love music and they've got really cool taste in it. They're just a really nice, normal couple, and now parents."
Didn't at least some part of her want to rebel and not do it? "I'll never see that experience as anything but incredible - seriously! Myself, my band, my crew, we'll never forget that night. It's quite an amazing honour to be able to sing the first dance for the future king."
Goulding isn't going to win any hipster credits, at least in Britain, for hanging out with the royal family. The rather polite legacy of Your Song has also proved a mixed blessing in her homeland. "I can see it made people suspicious, and also made me be seen in a certain way," she says. "But I still love it. When I recorded it I just listened to it over and over, it's such a beautiful song and I loved the way it was done and the way I sang on it. But it's true that I'm known much more for my electronic stuff in the US, which isn't the case here."
Does she believe in the old adage that there is less of a desire to knock artists in the States? She nods. "Everyone says that because it's true. It's a completely different attitude in America. Here, well, we're more cynical, I guess. I love where I come from, and I don't think I'll ever move from England, but..."
The dichotomy of Goulding's career runs right through her music and into her lyrics. While her first album Lights, as its title suggests, was largely ethereal and uplifting, she views her second album, Halcyon, "as quite a dark record. Even the happier songs like Joy are talking about my obsession with death. The lyrical content is quite stark."
She traces that seam of uncertainty and unhappiness back to elements of her upbringing, and in particular the paternal absence. Goulding has no idea if her father has heard her any of music. "I think the family situation gave us all the impetus to work really hard," she says. "And survive. Me and my siblings have all got a massive survival instinct, and this feeling that we've got nothing to fall back on.
''My siblings do very different stuff to me, but we all knew we needed to work our asses to get anywhere in life. It so happens I have a hell of a lot of drive to do well in whatever I did."
Her obvious determination and focus - traits much admired in America but often viewed somewhat less charitably in Britain - aren't restricted to music. Fanatical about running and exercising, Goulding's fitness levels mean she can "run around on stage for hours and not get tired. It's one of the incredible benefits. I'm not one of these people who likes to be still on stage, I like my shows to be absolutely full of energy and movement."
She is looking forward to catching some of next year's Commonwealth Games in Glasgow. More immediately, she fancies running another half marathon. That would presumably require quite a lot of training, I say. "Not really, I could probably run one tomorrow but I'd want to run it in a time I was happy with, or beat my best, which is currently one hour and 41 minutes. That's not bad, is it? I'm competitive like that."
That much is clear. Ambitious and driven, Goulding has no desire to stop confounding expectations just yet. Future plans include a "folk-based record, and I want to make a purely electronic album. I feel very lucky I can do both." She could well be on to something: two pop stars for the price of one.
Ellie Goulding plays the Usher Hall, Edinburgh, on Tuesday