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BARCELONA, Spain — Samsung has often been accused of being a clever copycat. In the case of its new flagship Galaxy S phones, announced Sunday at the Mobile World Congress in Barcelona, Spain, Samsung has created phones that unquestionably borrow on the most appealing elements of the iPhone. But they also stand out with their own impressive design twists.

The Samsung Galaxy S6 and Galaxy S6 Edge have been redesigned all in glass, dumping the removable plastic back cover that many complained felt cheap. The phone’s interface is simpler, there’s a greater emphasis on the camera and the fingerprint sensor, and Samsung announced that mobile payments would soon come to the phones in force.

Sounds a little like an iPhone 6, right? But the Galaxy S6 and S6 Edge are no mere clones, and the S6 Edge in particular brings a new style that actually makes the iPhone look conventional by comparison.

Samsung also announced a new version of its virtual reality headset, the Gear VR, to complement its new phones.

That phone features a curved screen that wraps down along each side of the phone for a sort of infinity pool effect. Samsung introduced the idea of the curved display with its Note Edge, released last year.

At the time, it was more a proof of concept than anything, and indeed, the curved sides don’t add significant functionality. There’s an alarm clock mode — a low-power display that shows the time and date on the curved edge, which is nice on a desk or by the side of the bed. You can add a list of contact shortcuts to the side screen as well, and since the display is curved on both sides, it can be customized for righties or lefties.

But the curved screen doesn’t really demand much extra functionality, because it’s just so nice to look at. With the Galaxy S6 and the S6 Edge lined up next to each other, the S6 almost disappears — you can’t keep your eyes off the Edge.

That’s not to take away from the S6, which gets its own design-oriented overhaul. Both phones are noticeably thinner and a bit lighter than the previous models, and the glass bodies are made of Corning Gorilla Glass 4. The S6 has a much thinner bezel than the S5, which also helps enhance the look of its screen.

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Samsung told me the phones should be durable enough to withstand a casual drop, although it will release a line of cases — including a translucent back case — for extra protection.

The translucent cases are designed to show off the phones’ colors. Each model will be available in black sapphire, white and a sort of pale gold that I found much too flashy. But the S6 can be had in a rich blue, and the S6 Edge in a truly lovely emerald green, and both of those colors make the phones look more like jewelry than electronics. They are extremely fancy — and the prices are likely to match.

In another convergence with the iPhone, the Galaxy S phones now come in three storage configurations: 32, 64 and 128 gigabytes. As a result, Samsung has eliminated the SD card slot, so you can’t expand your own internal storage — and it also means three price points. Samsung wouldn’t specify pricing, but told me the 32GB model was expected to start at the same price as the previous Galaxy S5.

That was about $200 with a new contract for most people. If iPhone pricing is our guide, the 128-gigabyte model could cost as much as $400 with a new contract. The cheapest iPhone 6, however, has just 16GB of storage with no expandable memory, so the low-end Galaxy S6 may prove a better value.

Samsung argued that not many people actually used SD cards to expand the storage in their phones, but the lack of options may frustrate some. And the all-glass design also takes away another big benefit of Samsung phones: the ability to swap out the battery. Samsung phone users often carry spares, and since battery life degrades over time, a decaying internal battery could mean you may have to replace the phone sooner.

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In terms of specs, the Galaxy S6 and S6 Edge are top of the line, with a new 64-bit processor, and increased and also more powerful internal memory. Samsung said it believes its active-matrix organic LED display boasts the world’s highest resolution (a claim that is hard to verify before other devices have been announced), and added that it is 20 percent brighter than the Galaxy S5.

To take advantage of that high-resolution screen, Samsung also announced a new version of its Gear VR virtual reality headset. The Gear VR works by plugging your phone — previously only the Note 4 was compatible — into the VR goggles and using the screen as the virtual reality display. The new model will allow the S6 to fit in the goggles, and the higher-resolution screen should reduce what’s known as the “screen door effect” where you can see space between individual pixels while watching virtual reality video.

The company also emphasized camera improvements. The 16 megapixel rear camera now has an improved lens and full-time optical image stabilization to make it perform faster and capture brighter, sharper images. The front camera goes from 2 megapixels to 5 megapixels, and there’s a new feature called fast-tracking auto focus that promises to make it easier to get in-focus shots of a moving subject.

In a particularly welcome change, you can now double-tap the home button on the phone to quickly launch the camera from any app or if the phone is locked.

The phones support wireless charging, using Samsung’s own accessories or most of the mats that you sometimes see in places like Starbucks. And the fingerprint sensor has been improved; instead of having to swipe down to unlock the phone, you simply hold your finger or thumb on the sensor (yes, like on the iPhone).

That fingerprint sensor will eventually power Samsung’s other big announcement: mobile payments, arriving on the S6 and S6 Edge, but not until summer. The feature is called (what else?) Samsung Pay, and will be based on the technology Samsung acquired in February when it bought the mobile wallet company LoopPay.

Samsung Pay, when it’s released, may be usable at more locations than Apple Pay or even Google Wallet, because the technology it uses for mobile payments can work over near-field communication (NFC) like Apple Pay, but can also mimic a traditional magnetic stripe card swipe.

That means Samsung Pay could theoretically be accepted at more stores — including those that haven’t yet upgraded their terminals to either NFC or the new chip-and-PIN terminals that will eventually do away with the card swipe. The company has teamed up with American Express, Visa, and MasterCard, and is working with major banks to get them to accept its payment system. Other details were sparse.

Samsung has recently struggled to keep buyers interested in its steady stream of new Galaxy models. The S5, for example, didn’t seem to add much over the S4. But with the Galaxy S6 and Galaxy S6 Edge, Samsung is moving in a beautiful and powerful new direction, and has indeed created something that looks and feels new and different.

Its high prices might deter some, but the Galaxy S6 accomplishes something important for Samsung: It’s a flagship phone that finally feels like a flagship.