There are many differences, but in short civil fraud is pursued by the victim(s) by way of a private action in the civil courts to seek recovery of the sums/assets which have been taken and/or the payment of compensation/damages to the victim(s). The decision in a civil trial will be made by a Judge. 

Criminal fraud is a criminal offence which will be prosecuted by the prosecuting authorities (If the prosecuting authorities are not prepared to bring proceedings, in certain circumstances an individual or an entity can bring a private prosecution in the criminal courts against a defendant (and in respect of other offences)). In the criminal courts (Magistrates’ Court or Crown Court) with the sanctions likely to be a fine and/or imprisonment. The decision in a criminal trial will be made by a jury.