The difference between an exchange and a transfer is the sequence of deposits
and withdrawals made in an exchange depends on the balances of the accounts
while those in a transfer do not. Exchange produces incorrect results without
additional serialization because another process can change the balances after
exchange's withdrawal and invalidate exchange's assumptions about the first
accounts balance which the later deposit is based on.

Transfer does not need additional serialization.

More generally, transfers from accounts with sufficient balances are
commutative because addition is commutative (withdraw = adding -amount to the
source balance and deposit = adding amount to the destination balance). This
means a set of transfers will produce the same final result no matter the
order (not true if a transfer can fail due to insufficient balance).

In contrast swapping is not commutative, so the final balances from a set of
exchanges can vary depending on the order of process execution.