Each implementation represents this channel state in slightly different ways internally and on disk.

This structure is not defined in any BOLT spec nor is it required to be the same for payment interoperability.

It just means you need to make a backup every time the channel is updated.

Your wallet or node implementation should handle this for you.

They will backup both pieces of state to your hard drive and ideally encrypted in the cloud as well.

While the keys used to create and sign each new commitment transaction can be backed up similarly to your on-chain keys, the latest commitment tx and revocation secrets cannot.