Continental Germanic and Scandinavian/Norse mythologies are often grouped together under Germanic mythology, usually a few deity names change but keeping the same roots, unlike Roman/Greek mythology. I am guessing that Continental Germanic is just a continuation of the Scandinavian mythology. Are there any major differences between the two?
Unfortunately, our knowledge of Continental Germanic mythology is extremely limited, due to the fragmentary nature of the available sources. We know that Continental Germanic mythology and Norse mythology both originated from the body of myths of the speakers of the Proto-Germanic language (the wikipedia page on Proto-Germanic folklore provides a very nice list of gods and entities with common origin), but it's hard to tell how much the two religions diverged over the centuries.
For example, let us consider the Second Merseburg Charm, which is perhaps the best example of Continental Germanic pagan belief (translation from Old High German by Benjamin W. Fortson):
Phol and Wodan were riding to the woods,
and the foot of Balder's foal was sprained
So Sinthgunt, Sunna's sister, conjured it;
and Frija, Volla's sister, conjured it;
and Wodan conjured it, as well he could [...]
It's easy to recognize in Wodan, Balder, Sunna, Frija, and Volla the corresponding Norse deities (Óðinn, Baldr, Sól, Frigg, and Fulla). But what about Sinthgunt? Was she an exclusively Continental Germanic goddess? Was she present in the Old Norse corpus with another name? Or was she a member of the Norse pantheon that simply does not appear in the sources at our disposal? We simply don't have enough elements to give definite answers.
More importantly, there is a growing consensus among scholars that the notion of a coherent, unified Norse mythology, as it is presented in most of the Norse corpus (i.e. the Prose and Poetic Eddas) is not an accurate representation of the religious beliefs in Viking Age Scandinavia. Similar considerations apply to Continental Germanic religions. Terry Gunnell deals with this issue in his article Pantheon? What Pantheon?, and says
[...] there is reason to consider that many of the gods known in the Germanic and Scandinavian world were tribally-, area-, or clan- (family-) related [...]
Arguably, part of the problem involves the way in which as scholars of pre-Christian Scandinavian and Germanic religions, we often casually jump from talking of tribal groups or family clans like those mentioned in works like Tacitus' Germania to discussing national units like those reflected in Snorri's Heimskringla, often forgetting that there must have been middle stages, and that the new nations were made up of earlier tribes/clans, all of which would have had different historical, social, cultural, and religious backgrounds, and associations with different local areas with their own environmental concerns.
That is, it doesn't make much sense to compare Scandinavian and Continental Germanic mythologies as if they were monolithic entities, when in reality they were a collection of tribal and family cults which could be very different from each other.