Not really. There is some overlap with certain bands like Suicidal Tendencies, but punk and metal musicians are generally trying to do different things.

For an example of a metal band that isn’t trying to sound like punk, here’s a doom metal band.

Candlemass, “Bewitched”

Punk in general emphasizes speed, but this song is pretty slow. The lyrics are about fantasy and magic, topics that aren’t covered in a lot of punk. While punks aren’t known for their high-quality music videos, I’m pretty sure a punk would explode in embarrassment if they were caught on camera in the above video. And that guitar solo is definitely a metal solo. Punk bands, even the exceptionally talented ones, rarely play flashy solos like that.

Speaking of exceptionally talented punk bands, here’s Bad Brains.

Bad Brains, “Banned in D.C.”

While the Candlemass song is 7:35, this punk song is just over 2 minutes. Punk songs are generally very fast and short. Instead of any dramatic poses or costumes, the lead singer simply dances onstage when he isn’t shouting into the mic. The lyrics, assuming you understand a word he’s saying, are about a real-life event that happened to the band. While Bad Brains has an excellent guitarist, his solo isn’t particularly flashy compared to the Candlemass solo because it doesn’t need to be.

There’s a significant difference in attitude between the two songs I used as examples.

The metal song is about subject matter that might make certain listeners uncomfortable, but I doubt they care what non-fans think.

Can't you see the devil in me?
Just take a look in my eyes
I will play for you this wicked melody
Its magic will reach for your soul

[1]

On the other hand, the punk song is directly addressed to the venues that banned the band. They want to express their scorn for people they don’t like.

And if you ban us from your clubs
It's the right time, the right mind
And if you think we really care, you won't find in my mind
No! You can't afford, to close your doors, so soon no more

[2]

Punk and metal are not the same thing. The musical styles are different, and so are the attitudes that drive the musicians.

Footnotes