The distinction is rather academic with ruby and rails. 90% of the answers to "how do I do this in ruby" on forums are actually "how to do this with rails" answers, but they never mention that little detail, because who'd ever write a ruby program without rails, right? Trying to find straight ruby answers is annoying as hell.
I've had frustrations with certain "ruby" libraries requiring methods like "blank?" (IIRC) that are provided only via Rails, not Ruby. It made developing on a machine that Ruby but not rails rather annoying.