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Here's the simplest mental model:

Lightning: two parties lock funds in a shared box. You and your channel partner can update the balance between yourselves directly. No third party. Finality is provable on-chain at any time.

Ark: an operator holds a tree of exit tickets — yours is a leaf. You can broadcast your leaf to claim sats on-chain whenever you want. The catch: your ticket has an expiry, so you have to periodically check in with the Ark server to refresh it. Go dormant long enough without refreshing, and the operator can sweep. Liveness requirement.

Spark: you and the operator each hold half a key. A transaction is valid when both halves sign. When you send to someone, the operator is supposed to forget their old half of your key — otherwise they could collude with you to double-spend. You're trusting the operator to be a selective amnesiac.

The key difference is the failure mode: Ark punishes you for going offline (expired timelock). Spark punishes you if the operator turns dishonest (key deletion failure). Lightning's failure mode is just: don't broadcast a stale state, which is verifiable without trusting anyone.