On my laptop I use Lightroom & Lightroom Classic. I am told that Lightroom Classic can be used on 2 devices. How do I get it on my phone. I downloaded the free Lightroom from the App Store. Is that different to the version I pay for.

Lightroom Classic cannot run on an iPhone. What you downloaded from the app store is what you need, and the only Lightroom for iPhone that is available. It is free with your Lightroom Classic subscription, but it is not identical to Lightroom Classic. It looks more like Lightroom and it syncs with Lightroom if you simply log in with your same account. Don’t worry, it doesn’t count in those two devices.