Distributed systems usually suffer from the so called double spending problem, there should not be two transactions applied to the same account in the same round. There might be several strategies to be followed based on the exact ledger storage implementation, however from a consensus point of view usually a superset of double spending is used, which is a common ordering of the transactions in a way that each node sees exactly the same order of transactions. This implies actually that there is no double spending, because if there are two transactions applied to the same account or unspent transaction, the first one can be chosen as valid and the second one as double spend and the same order will be used by every node in the consensus. The other direction will not hold however, there might be consensus algorithm avoiding double spend without a requirement of full ordering of the transactions. Actually, from a theoretical point of view only partial order is required, creating an order of the transactions that want to change the same account.
Certainly, from a theoretical basis, the situation can be a little bit more complicated if we consider general smart contracts as well instead of cryptocurrency transfer. At smart contracts a transaction might consume information of an account and modifies another one. It is important here to have consistency, instead of double spending, like a transaction should not be dependent on the value of an account if another transaction tries to write the same account variable.
Certainly, from a theoretical basis, the situation can be a little bit more complicated if we consider general smart contracts as well instead of cryptocurrency transfer. At smart contracts a transaction might consume information of an account and modifies another one. It is important here to have consistency, instead of double spending, like a transaction should not be dependent on the value of an account if another transaction tries to write the same account variable.
