I've always considered a weeabo to be an individual whom utilizes basic Japanese words in casual conversation without knowing fluent Japanese. AKA: An individual whom has no desire to understand the language, but utilizes words like "Kawaii" because they think it's cute.
Example:
1」You are so sugoi, i like that desu.
Versus.
2」 あなたわほんとにすごいです。
Most people use "Otaku" as a reference to their lifestyle, they're obsessed with anime, and as such live for it. I personally don't consider the use of the term"Otaku" to be weeabo specific. Just like "Schadenfreude" or "Yandere", it's a foreign word depicting a personality trait, or interest.
In the end to each their own.