You said, the core Karate principles are the same everywhere.
And i say: Wado Ryu adds some principles from koryu bujutsu (old martial arts, before 1868) and that makes a big difference.
It is not, that we have other combinations, like for example shotokan do Soto Uke / Gyakuzuki and we do Uchi Uke / Gyakuzuki.
It is not about this.
It is like say you can think, so you think the same way as every one else.
Then i say: "But i had a friend, Albert, and he thought different than you."
And you say "we all have different thougts, but we think all in the same way in our mind"
And then i say: "But my friend Albert made complicated thoughts, he made thought-experiments in his head"
And you say "at the end, every person can think complicated."
And i say "yeah, but my friend Albert Einstein formulated Special Relativity in his head and General Relativity and all other 100 billion people which lived in the world in the last 200'000 years did not, so he thinks somehow different."
and you say "but i can also think about relativity"
So in this example: Do we think all in the same way? Somehow yes. But some people are more intelligent than others. And some think total in different directions.
Other example:
Let us say, a friend of mine can run 100 meters in 9,7 seconds and is one of the fastest persons in the world. You would say "All people can run fast, when there are young and slim".
Yeah, you are right, but not all people in the world could do 100 meters in 9,7 seconds when they were young, so it is a difference in running technique but also in the quality of training and quality of result.
The same is with Wado.
Yeah, other styles also have