That is quite wrong.
There are usually two implications meant by melodic death metal, which causes much argument between the factions advocating either style over the other:
1. Melo-death/"Gothenburg" - Dark Tranquillity, earlier Soilwork, earlier In Flames, Detonation, later At The Gates, etc., etc. Bands don't have to be from Gothenburg or even Sweden or even Europe, though, Gothenburg melo-death tends to be semi-pejorative/offensive but it shouldn't be taken or used as such. Bands lumped in this genre tend to display a distinctly "power metal" outlook on things, rather than a death metal (implied chaos, in this case) approach. There is also an endless argument as to whether or not CoB are melo-death or power metal, since they most certainly blur the line, but the band has speed metal roots on Hatebreeder et al so people mainly refer to them as power metal with harsh vocals. Interestingly, bands that piggyback on their style are called melo-death (Kalmah, Skyfire, Mors Principium Est; anything fast, melodic, keyboardy, and commanding sounding instead of being soaring and epic like most power metal).
Melodic death metal: This is death metal with a focus on melody and melodic/harmonic structures. It still retains the innately chaotic (that word again) feel of death metal, but with a more "accessible" edge. Even still, that is not to say their senses of melody make them automatically appealing; Arghoslent, for instance, are not melo-death, nor are they really pure melodic death metal (a lot of the time they are though)...there's a LOT of old-school heavy metal and some thrash in their sound here and there.
This is basically semantics. I wish lovers of both styles (such as me) could become more prevalent and less people who stick to one camp and close their mind to/berate fans of the other...