Much the same way that all thumbs are fingers, but not all fingers are thumbs, today’s word (using the base understanding) can be taken in the context of a previous term: all weeaboos are otaku, but not all otaku are weeaboos.
If you are feeling a bit lost or if you didn’t see the previous word “weeaboo” (you should really read that one too), don’t worry, it’s not as bad as it sounds. In fact, in many ways, we are all differing and vary version of otaku; thankfully, it’s a part of what makes us who we are.
Literally translated, the Japanese term otaku (お宅) means ‘you’; however, in a larger and more honorific sense, it also means your house or family. While there are competing theories about how the word originated in usage – some point to the anime Macross, the 1983 work Research in “Otaku” by humorist/essayist Akio Nakamori, or even recorded conversations in the late 1970’s between animators Haruhiko Mikimoto and Shōji Kawamori – most plausible explanations point to anime/manga in the late 70s/early 80s.
With regard to being popularised in English, like many other Japanese cultural terms, our word can be traced back to 2003 and the beginning of 4chan, which was originally set up as an English-language imageboard website paralleling the Japanese 2chan, which focused on topics of anime and manga.
Sure, there is no denying that our word has its base in the world of anime and manga, but, in the most general of terms, an otaku is simply someone who would be considered a hobbyist or enthusiast. Expounding on that, the understanding of a ‘family or house’ that comes along with the basic meaning of otaku would be the social group to which the enthusiast belongs. Still, in many cases, by being a Japanese loanword, otaku is traditionally based around facets of Japanese culture, yet it doesn’t embrace the entire culture in a way that weeaboos do.
As far as whether it is considered a positive or a negative epithet, that really depends on who you’re asking.
Many within the anime/manga community wear the term proudly, even going so far as using it to address each other, which, linguistically speaking, is highly (and overly) formal.
On the other hand, outside of the community, especially in Japan itself, the term is used more disrespectfully, often denoting someone who, aside from just having an interest or preference, has trouble relating with reality or social situations outside of their sphere of interest.
If there’s a lesson to be learned from this, it’s that it is fine to have a hobby or interest, but the key is keeping it in perspective.