A centralized PoA network: is a network where a central authority chooses to include new nodes in the current group of validators. A famous example of such an approach is Ripple, its RippleNet network being used for global international money transfers.
A decentralized PoA network: lets the community (i.e. existing validators) choose to include or exclude a new node in their group. iXXo implements this approach by providing smart contracts for a miner to vote on network extension or to ban some wrongdoing validators.
Some might argue that PoA protocols are somewhat centralized, preferring dPoS (delegated Proof of Stake) such as for the Lisk, Cosmos Network, EOS, and ARK blockchains.
It is to be remembered that in dPoS protocols nodes only vote to select a producer, and the real consensus happens on a Proof of Authority level, with a few selected block-producing nodes. In the dPoS consensus, the staking mechanism ensures that producing nodes are doing an honest job.