Like all enzymes, DNA polymerase is substrate-specific. DNA polymerase cannot extend a single strand of DNA; it needs at least a short segment of double-stranded DNA at the outset.
As its name implies, DNA polymerase incorporates deoxyribonucleotides into the new strand. RNA polymerase incorporates ribonucleotides.
These differences mean that DNA polymerase is active when new DNA strands are formed, as in DNA replication, and RNA polymerase is active when new RNA is formed, as in transcription.