No, those are two completely different formats. HDDVD is as well, which failed. Saying those are the same format would be like saying VHS and Betamax were the same format because they were both video tapes.
“No, those are two completely different formats.”
A BluRay is a DVD. Specifically a DVD encoded in the BluRay format.
A DVD is a physical disk, not a format.
“Saying those are the same format would be like saying VHS and Betamax were the same format because they were both video tapes.”
Saying a BluRay is not a DVD is like saying VHS is not a video tape.