So, would the below count as a "real beard", simply because it completely covers my face (meaning it's not just stubble), even though it's not much over a quarter inch long? Just out of curiosity, you understand.
Yes, I would classify that as a real beard, albeit a pretty short one. It would certainly not be classified as mere stubble, and you obviously groom it, trim it and shape it, etc. But then again, it has a long way to go before being able to compete with 19th century beards!

Actually, the length you show there is about the same length I have worn mine for the last 13 years. But a few months ago I decided to grow out a winter beard, just for kicks.

This is my 'normal' beard length:


And my winter beard in progress, with shocks of grey showing up:


I'm thinking I'll let it go until it looks 19th-century-like:


(by the way, we need a bearded emoticon here!)