No. I didn't say they were confused at all. In fact, they knew there was a difference, hence the creation of the term "space-time."So ... True Time is a non-real thing that always existed and will always exist, but is not observable, and it's what laymen are thinking of when they talk about time, but it's scientists who are confused.
And by non-real, I mean it's purely conceptional. It can't be contorted, distorted, or altered due to things like gravity, distance, or speed. It's just a base measurement, only one we can't really do anything with because space-time obfuscates it so heavily. We simply don't have the means (or any real motivation to find the means) yet.
Especially when people like you pop up and try to mock the concept. In fact, it's actually pretty sad how pigheaded so many physicists (real or armchair) are. I mean, they had to make up dark matter/energy just to prove how awesome their math is; completely ignoring the fact that they actually did have to make it up in order to do so. But hey, they did, and it kinda works, so problem solved! *thumbs up* There totally wasn't anything before the Big Bang though. True story. Nothing wrong with that idea at all!
Snarkiness aside, I'll sum it up for you: We focus on space-time because it's what we can observe and which affects everything we can observe and measure. True time is 100% just a concept; there was a time before the Big Bang, there was a time when the Big Bang happened, and there was a time after the Big Bang. We just have no way whatsoever to measure, observe, or demonstrate it. You know, just like tons of other things that exist only as a concept.