I don't know that there's an 'official' definition. Fowler's article was the first piece that I read on DI. If that's not authoritative enough for you, I don't see how SO will improve on that.
What does 'looked through' mean to you? How much of the documentation have you read? Have you tried writing any applications with it? You've already done a pretty good job of investigating this for yourself if you've written code with Spring and Guice. If you've just read a few articles that Google brought back you've got more to do.
'Context' in Spring means the factory used to instantiate objects for you. I usually have one per application or web app. My application is usually the 'context' in which objects are created.
'lifecycle' is no different for DI - it has to do with when an object is created, initialized, used, and destroyed.
Components are data and operations in a single software artifact. Services are special kinds of components that perform business-significant operations, usually distributed on a network. Services are usually components, but not all components are services. They aren't synonyms.
You can write components or services without a DI framework. If it helps you to call injected objects 'components', be my guest.
I'm curious: why the emphasis on names for these things? Naming is certainly important, but it's not the primary issue with DI.