"Supernova" is the explosion or the resulting celestial body? Is it incorrect to call the explosion "supernova"?

Is it incorrect to call the explosion “supernova”?

Yes and no.

Better said, the explosion is the very first part of a supernova. While the explosion lasts for but a few seconds to a few hundreds of seconds, a supernova can last for hundreds of days. What we see visibly as a supernova are the after effects of that explosion. The explosion can create lots and lots of stuff moving at very high velocities, and lots and lots of highly radioactive nuclei.

If the star had outgassed material prior to the explosion, the highly kinetic material produced by the explosion runs into that previously outgassed material and makes it glow. This takes some time to cool down. The radioactive material produced during the short course of the explosion proper takes time to decay to stable elements. This radioactive decay eventually produces gamma rays, some of which is absorbed by the nearby material, heating it, thereby eventually producing thermal radiation.

For example, a type Ia supernova produces a large amount of nickel-56. This decays to cobalt-56 with a half-life of about 6 days, which in decays to iron-56 with a half-life of about 77 days. The heating that results from these decays is what we see, and because it is so predictable, this is makes type Ia supernovae a fantastic standard candle.