The active set is the group of validators actively participating in securing a blockchain network, eligible to be selected to perform work and to receive rewards for doing so. A validator could be registered on the network, but not a part of the active set, if they fail to meet certain requirements for participating in the network's consensus—such as by not having enough value staked.
The Beacon Chain introduces proof of stake (PoS) to the Ethereum protocol and coordinates the network's security. In September of 2022 the Beacon Chain was merged with the original Ethereum proof of work (PoW) chain, transitioning Ethereum's consensus from PoW to PoS.
Blockchain infrastructure is a broad category for the resources and frameworks that make a blockchain network function. Infrastructure includes nodes/validators, clients, hardware and cloud-based systems, software implementations, security programs, and more.