Power cord for iPhone 13

Both of them have the same Lightning connector on the end that connects to the phone.

The cord that came with an iPhone X had a USB connector on the end that connects to the power adapter.

The cord that comes with an iPhone 13 has a USB-C connector on the end that connects to the power adapter.

You can use the iPhone X cord (and the USB power adapter for the iPhone X) with an iPhone 13.

No.

The iPhone 13 uses a cord that has a Lightning connector on the end that connects to the phone.

The other end can be either USB to connect to older power adapters and devices or it can be USB-C to connect to newer power adapters and devices.

Are you saying the iPhone 13 uses a cord that has a lightning plug on each end?

The iPhone cable that came with your 13 is a Lightning to USB-C that supports fast charging.

The one with your iPhone X is a Lightning to USB-A cable and does not support fast charging.