No, two transactions must never share the same ID. It is the only identififier that can be used to differentiate between two transactions. Fortunately, the ID is generated with a cryptographic hash from the raw transaction, so this case will never happen in practice.
No, hosseinimr93 is right with his reply above.
Two transactions cannot share the same ID if the original transaction is not yet fully spent. In other words, if a transaction currently exists which has at least one unspent output, then no new transaction can share its transaction ID. However, once all the outputs of a transaction are spent, and so no outputs from that transaction remain in the UTXO set, then a second transaction can indeed reuse that same transaction ID.
This distinction is important, because without it, pruned nodes could not exist. If the stipulation was that any new transaction cannot share the ID of
any previous transaction, then every node
must keep a record of
every previous transaction, and so could not be pruned. However, with the wording of BIP30, which allows transaction IDs to be reused once fully spent, then pruned nodes do not need to keep a record of all previous transactions, and indeed only need to keep a record of the UTXO set, which they do anyway.