I have to give a long answer because this question almost demands an essay on The Evolution Of Punk.
The term Punk Rock was being used among rock critics in the U.S. in the very-early '70s, long before Malcolm McClaren and the Sex Pistols were even a glint in the music world's eye. The term was first applied to the garage bands and one-hit wonders that sprung up in the mid-60s in America and elsewhere, mostly inspired by the raw R&B-inspired rock that came to the fore as part of the so-called British Invasion (after The Beatles "conquered" America and other groups followed). That explosion of music was first documented by Lenny Kaye (who later played guitar with Patti Smith) on a double-vinyl album in 1972 called 'Nuggets: Original Artyfacts From The First Psychedelic Era 1965-1968'. It featured everything from pure-Beatles-inspired pop ('Lies' by The Knickerbockers) to over-the-top-psychedelic rave-ups ('You're Gonna Miss Me' by The Thirteenth Floor Elevators).
The reason I'm bringing this up is that Punk Rock to me has always been a very broad category but at its essence it is high-energy, economical songs - sometimes poppy, sometimes trippy, sometimes primitive but never pretentious: it's immediate and in-your-face even when it's slow or sombre. What most people think of when you say Punk is the Sex Pistols but it goes back much further than that.
The Stooges and the MC5 continued the American punk tradition and later the New York Dolls and even Alice Cooper were being described as punk (though mainly it was a term applied to 60s garage bands). Malcolm McClaren's main interest was fashion and he had a clothing store in London called 'Let It Rock' specializing in 1950s music-inspired clothing which later became 'Live Fast, Die Young'. McClaren went to live in NYC in 1975 and while he was there he took over management of the New York Dolls, a brilliant group who, sadly, were on their last legs. Johnny Thunders and Jerry Nolan (guitarist and drummer) had recently quit and the band had failed to find success with their two brilliant albums. In an attempt to raise their profile, McClaren tried to inject some controversy into the band's image by making them dress in matching red leather outfits, declaring they were communists (how outrageous!) they also performed using the hammer and sickle flag of the Soviet Union as a backdrop. Nobody paid any attention to these desperate shenanigans and the band broke up shortly afterwards.
While he was in New York, McClaren had caught wind of the CBGBs scene and took note of the term "Punk Rock" that was being bandied about by critics when writing about current bands like The Dictators, The Ramones and others. At this time Johnny Thunders and Jerry Nolan were in The Heartbreakers (not Tom Petty's band) with Richard Hell on bass, who'd previously been with legendary CBGBs pioneers Television. At one gig Richard wore a ripped T-shirt held together by safety pins with the words "Please kill me" scrawled on it (which is the title of a must-read book about the NYC punk scene). One of Richard's new songs at the time was 'Blank Generation' which became an anthem of sorts and was later a term used for members of the '70s punk movement.
Malcolm saw all of this and hightailed it back to London with his new (stolen) fashion statement: ripped clothes adorned with safety pins and confronting slogans and images, all tied together with a "new" marketing brand - Punk Rock! He immediately changed the name of his clothing shop 'Live Fast, Die Young' to 'Sex' and he added bondage gear and other "outrageous" trimmings to create his new "Punk" fashions. All he needed now was a band to help him sell his fashion trend to the public. Luckily for him, a few snotty teenagers who loved Bowie, Roxy Music and Mark Bolan used to hang around his shop and eventually he coaxed a few of them into becoming the Sex Pistols.
So, in answer to your question, to me Power Pop and Punk are incredibly closely-related. The Ramones, let's face it, are the single most-important band in the history of 70s Punk from a musical perspective (the Pistols and others are more notorious). The Sex Pistols and The Clash all copied The Ramones because they showed everyone how to play cool music without relying on unnecessary "musicianship" (overly-technical playing). For a bunch of amateurs and "wanna-be"s that was a revelation. Plus, The Ramones were funny. Their irreverent attitude and so-dumb-they're-smart lyrics were just as important to everything that followed as was their invention of buzzsaw guitar riffing and simple, slamming chords and rhythm patterns.
The Ramones were inspired by the Beach Boys, The Dictators, The New York Dolls and even the Bay City Rollers (forgotten teen-idol bubblegum band from Scotland). The Ramones songs were filled with pop melodies but married to an aggressive sound.
That's Punk Rock to me.