**Phage DNA** is the DNA in a bacteriophage.
**Recombinant DNA** is synthetically combined DNA used in genetic engineering.
In your case, since the phage's DNA is used as a vector, the phage DNA _is_ the recombinant DNA, but that does not mean every phage's DNA is recombinant, since phages occur naturally. The point is, the phage DNA was altered to _become_ recombinant DNA.