Otaku and weaboos are not the same thing.
Otaku means someone who is obsessed with a particular thing or hobby to the point where it effects their social lives. You can be a baseball otaku, a movie otaku, a video game otaku, etc. Westerners for some reason have tried to make this word a good thing and refer to themselves as otaku, when it really isn't a good thing at all. It means you have an unhealthy obsession.
Weaboo is something strictly made for westerners and is an insult. It was originnally "wapanese" which means "white person obsessed with Japanese culture" and its was kind of a slur. On 4chan, people started using this a lot, but then 4chan added a filter that prevented people from saying it and changed "Wapanese" to "Weaboo". Still means the same thing, but has lost its meaning now as people refer to any casual fan of anime and manga, or anyone interested in Japanese culture at all, as a weaboo. What it really means is anyone who glorifies Japanese culture, and thinks Japan is some kind of perfect fantasy land like in anime or manga. They refuse to listen to anything negative said about the country and believe anything that comes out of Japan is superior to anything made in the west.