There is no yesterday and today "heaviness". "Heavy metal" is both the name of all metal genres and it is the general tone of 70's and 80's metal. When Metallica used heavier riffing than Black Sabbath they made a new "genre" in "heavy metal" and were named Thrash. When Death changed the singing tone the new tone was called Death.
When Meshuggah used the monotonous D-jent heavy riffing sound they were called Djent.
They are all heavy metal for the fact that all of them are heavier and different than rock and classic hard rock.
Black Sabbath is heavy metal. Black Sabbath and rainbow and Dio are the godfathers of heavy metal. Having heavier sounds now doesn't make them rock or hard rock.
I think they are Hard Rock... and probably pioners of it... I disagree wid term "Classic Rock" since Classic Rock doesn't exist as a genre... those bands people mention as "Classic Rock" they were 60s-70s Psychedelic Rock/Progressive Rock mostly... they're just considered Classic by today's standards...
Anyway Black Sabbath were harder and edgier than other popular bands by dat time... like The Doors or Deep Purple... so I guess Hard Rock suits 'em better... I think heavy-metal didn't exist when Black Sabbath appeared (early 70s)... but Ozzy Osburne's solo works can be considered Heavy Metal... or even Glam Metal some of 'em...
Was going to say Crazy Train is Ozzy... but anyways, they have changed over the years. To begin with I'd say they were bordering on prog-rock but not quite as progressive as many others, such as Pink Floyd. They're quite soft as far as heavy rock goes, Faeries wear boots is a gentle instrumental track but it's on an album with other tunes which are a bit heavier, but still not what I would call 'heavy'. I don't think any of those categories really describe the sound as a whole. You listen to A National Acrobat and then listen to Paranoid, the lyric content is quite different, as is the pace and feel... they're a band that were going so long that the style changed a lot and I don't think one category can cover them.
I was 15 when their first album came out. My best friend bought it and played it for me, but I had been heavy into Cream for a few years by then. Compared to Clapton, Bruce and Baker, Black Sabbath was a pimple on the buttocks of progress. Of course, I was an aspiring musician myself at the time, so I was a bit snobbish.
They were and always will be metal, they kind of fall into classic rock now too. So all of the above I guess. By the way, Crazy train isn't Black Sabbath, it was Ozzy's solo act. Black Sabbath had numerous lead singers over the years, Ozzy was frontman from 69-77 or 78, and rejoined in the early 2000s I think.
Black Sabbath were predominantly hard rock, but they certainly helped setting in stone genres such as doom metal and heavy metal. They expanded upon their usual slow heavy compositions to faster ones ocasionally.
Back in the day we didn't have all these invented subgenres that we do now. Rock and metal had a shared fanbase. Sabbath had their background in Hard Rock, but for me they were the first Heavy Metal band.