The opposite was true actually - the original iPhone couldn't run third-party applications at all.

What it did have was a much bigger and better touchscreen that didn't need a stylus. (Even that wasn't really a technical innovation per se - rather it was the willingness to charge over twice as much as previous phones that made it possible).

Yeah - capacitive touch tech was far from new, but it was still super expensive compared to resistive. Price made it largely not an option until around the time that Apple adopted it (which they were definitely ahead of the curve on, and they made fantastic use of it). It was pretty clear at the time that nobody was all that fond of styluses, but they were the sole pragmatic option available then.

That, and many people were glad to have plastic screens - iPhones shattering because you looked at them too enthusiastically was a source of many lols and many expensive repairs / re-purchases. The early iPhones still scratched nearly as easily (keys or sand were more than sufficient), but they were nowhere near as durable overall. Decent screen durability, screen protectors, and protective cases took years to arrive - the gorilla glass of the time was far, far more fragile than it is now.

To be precise, the original iPhone can run third-party apps, but couldn’t from the beginning. The AppStore was introduced with iPhone OS 2 a year after the launch.

The iPhone was most certainly not the most full OS at the time.

Can you explain what capabilities it had that were different?

all the other baby devices had copy/paste functionality though.