Currently, in the Cosmos Network, a zone is an independent Tendermint consensus blockchain, and the security comes from its own PoS. (Should Cosmos successfully implement its Interchain Shared Security  model, this may expand sometime in the future.)

Polkadot is a heterogeneous sharded blockchain. Parachains are not blockchains with independent consensus, but shards. The Relay Chain does all the validation and guarantees that every parachain has the same level of security.

An appchain can determine its own security level by adjusting the block rewards that it pays to validators.