Bitcoin Q&A: SegWit, Schnorr, Taproot, and Graftroot

Why are there different types of SegWit addresses? How much space should we expect to gain with Schnorr signatures and signature aggregation? How does Taproot, as proposed by Pieter Wuille, work and compare with zero-knowledge proofs? What is the implementation timeline for Schnorr signatures, confidential transactions, Taproot, and Graftroot?