Below definitions are quoted from Akka Documentation
at-most-once delivery
means that for each message handed to the mechanism, that message is
delivered zero or one times; in more casual terms it means that
messages may be lost.
at-least-once delivery
means that for each message handed to the mechanism potentially
multiple attempts are made at delivering it, such that at least one
succeeds; again, in more casual terms this means that messages may be
duplicated but not lost.
exactly-once delivery
means that for each message handed to the mechanism exactly one
delivery is made to the recipient; the message can neither be lost nor
duplicated.
The first one is the cheapest—highest performance, least implementation overhead—because it can be done in a fire-and-forget fashion without keeping state at the sending end or in the transport mechanism. The second one requires retries to counter transport losses, which means keeping state at the sending end and having an acknowledgement mechanism at the receiving end. The third is most expensive—and has consequently worst performance—because in addition to the second it requires state to be kept at the receiving end in order to filter out duplicate deliveries