How do I check all subscriptions on my iPhone?

You go to Settings ➜ Account (top of Settings) ➜ Subscriptions.

All your active subscriptions and recently cancelled subscriptions will be listed there.

Subscriptions are tied to your Apple account, not a specific device though.

It means there no other subscriptions associated with that Apple Account.

Again, subscriptions are not tied to a specific device. They are tied to your Apple account, so they can be used on different devices.

As mentioned by Jim, you can subscribe to other things outside of Apple's platform, and they would not appear there, but can still charge you.

If you have charges on your payment method for specific things, then those don't come from Apple. Apple charges appear as "apple.com/bill" only.

Any other charges that say what they are for, do not come from Apple and as such would not appear in the subscription list there so cannot be managed from there.

It means you have no other subscriptions with your Apple Account. You can certainly use your device to sign up for any subscription you want on a website where it will not show there as being managed by Apple where it can be easily cancelled. For example, you can go to Netflix and subscribe for their service or subscribe to Amazon Prime and none of those would have anything to do with Apple and would not appear on your Apple Account subscriptions. Subscriptions are NOT device specific, what you see are the subscriptions managed by Apple on your Apple Account..