Cloning vectors tend to be slower growing so they are easier to pick as single colonies. Expression vectors can often have additional transcription factors added to them to allow for expression of genes of interest using a promoter that is not used by the cloning vector (often used if the product is toxic).
The 2 vectors make it possible to insert a DNA sequence. However, as its name suggests, an expression vector allows, after insertion of a gene, to express it in order to produce its protein, therefore this vector, it also contains the sequences for regulating the epression and especially it contains a promoter upstream of the inserted gene.
Cloning vectors are generally high copy number so that you can get more colonies and high amount of plasmid during plasmid isolation steps. Expression vector as the name suggests is efficient for protein expression as others have already mentioned