Back when I first played this it never occurred to me that it was anything but a direct sequel to Simon's Quest. This is mainly due to how closely the ending of Simon's Quest matched up to the intro of SCVIV.
The "best" ending to Simon's Quest (which you would think means is the "true" ending since its the hardest to achieve) is the view of the grave, followed by Dracula's hand coming up out of it, implying that he's not dead and Simon hasn't heard the last of him. Then the third game in the NES trilogy was the Trevor prequel that had nothing to do with Simon, and the GB games from that time also featured a different Belmont that had nothing to do with Simon. So there was basically no real closure to Simon's story (especially when you consider the incredibly anticlimactic final boss fight in Simon's Quest).
Now you have Super Castlevania IV, which opens with the almost identical grave that we last saw Dracula's hand come up out of, and its struck by lightening and we are then informed that Dracula has risen and "once again" Simon would challenge him. I get it that the intro also told us "it has been 100 years since the Belmonts last battled Dracula", but I always took this as just establishing the whole "Dracula rises every 100 years" thing, not literally meaning he just rose and Simon has never fought him yet.
Considering the above, I always liked to think of SCVIV as a direct sequel to Simon's Quest instead of a remake of the original, for the following reasons:
-SCVIV intro follows "best" SQ ending so well, as described above.
-Simon's Quest final battle/ending was unsatisfying, SCVIV gives better closure to Simon's story.
-If I want to play all the games in order to experience the full Castlevania story, I am forced to skip either the original or SCVIV because they tell the same story... when those are two of the greatest Castlevania games!
I understand that the original Japanese version has SCVIV as a remake and the US version hinted at it as a sequel, and to hammer that point home Iga made it "official" in his canon that its a remake. But back in those early days, the story was still open to interpretation, the whole complex Iga canon hadn't come into play yet. And these days, with the new games "re-imagining" old characters and story concepts, it seems that Iga's canon isn't worth the paper it's printed on. This is the era of interpreting the Castlevania story how you choose... if MercurySteam can do it, why can't we?
So to me, Super Castlevania IV will always be the epic conclusion to the Simon trilogy, the final battle between him and Dracula after their first two encounters, and the fight that after two failed attempts finally puts Dracula back in the ground for the next 100 years so Simon can live happily ever after making babies for the next generation. If you prefer to think of it as a remake, that's fine too. To me there's no wrong answer, it's all up to how each individual interprets things.