What Schnorr changes
Schnorr verification has a linear algebraic form and supports batch verification and carefully designed multisignature protocols. Its security still depends on sound nonce generation and the exact BIP 340 encoding.
Aggregation needs a protocol
Adding public keys or partial signatures naively can enable rogue-key or nonce attacks. MuSig-style coordination adds coefficient, nonce and transcript rules; a Taproot key does not prove that multiple people created it.
Taproot commits to key and tree
BIP 341 tweaks an internal public key with a commitment to an optional Merkle tree. The resulting P2TR output looks the same on chain until spent and can use a single key-path signature when participants cooperate.
Privacy is conditional
A script-path spend reveals the chosen leaf and Merkle proof, not every unused branch. That can save data and hide alternatives, but transaction amounts, timing and input links remain public; Taproot is not automatic anonymity.