Yeah, guilty as charged. I’m still kind of new at this.
Ions and isotopes are just a couple of ways H atoms can be unique. A hydrogen atom in the Pleiades and a hydrogen atom in my bottle of water may be different in their chemical composition*, their proximity to large masses, their energy level, and so on. These attributes don’t necessarily alter their intrinsic quantum nature, but after observation you can declare that these two atoms are different and distinct. If you isolate the atoms and observe them under strict and sterile conditions, it may become difficult or impossible to tell them apart, but this result is in part an artifact of the observation.
Well, let’s get another definition out of the way. Drake’s equation is an estimate of the number of extraterrestreal civilizations we might communicate with. (Presumably, the number of existing civilizations is a bit higher, but irrelevant since we we have no contact with them.)
Assuming we’re talking about conventional methods of communication - any combination of audio, visual, radio, etc. - then sure, I’d imagine that the concept of stars (and nebulae and other extrasolar phenomenon that might obscure interstellar line-of-sight) would be understood.
Which brings me around to another criticism I have about Drake’s equation. It doesn’t take distance or Olber’s paradox into consideration. Light propogates so slowly across the universe (and/or is blocked in transit by dark matter), that entire chunks of the night sky are dark. We can just barely discern light reflected from planets orbiting nearby stars. It’s entirely possible that Drake is correct, there are plenty of civilizations out there willing to chat with us. But we’re not advanced enough to listen.
Getting back to your OP, you’re essentially asking “are we alone?” If we are alone, how can we reconcile this unique event against the vastness of the universe? I really have no clue. I just don’t think we have enough information.
Personally, I’m inclined to say no we’re not alone, but that we currently lack the means to verify this. I also currently lack the means to back up my opinion. 
- Not “composition” - the word I’m looking for is like the opposite of “composition”. As in one atom is part of a water molecule, and the other atom is a bare proton. I can’t think of the word I’m looking for. Arg.