This paragraph from Lehninger's Principles of Biochemistry (in my opinion the best textbook on biochemistry) is very didactic:
DNA Is Degraded by Nucleases
To explain the enzymology of DNA replication, we first introduce the enzymes that degrade DNA rather than synthesize it. These enzymes are known as nucleases, or DNases if they are specific for DNA rather than RNA. Every cell contains several different nucleases, belonging to two broad classes: exonucleases and endonucleases. Exonucleases degrade nucleic acids from one end of the molecule. Many operate in only the 5'→3' or the 3'→5' direction, removing nucleotides only from the 5' or the 3' end, respectively, of one strand of a double stranded nucleic acid or of a single-stranded DNA. Endonucleases can begin to degrade at specific internal sites in a nucleic acid strand or molecule, reducing it to smaller and smaller fragments. A few exonucleases and endonucleases degrade only single-stranded DNA. There are a few important classes of endonucleases that cleave only at specific nucleotide sequences (such as the restriction endonucleases that are so important in biotechnology; see Chapter 9, Fig. 9–3).
We can conclude that restriction endonucleases (or restriction enzymes) are a type of endonuclease, and that endonucleases are a type of DNAse. So, all restriction enzymes are DNAses, but not all DNAses are restriction enzymes.
Besides that, we can conclude that your initial statement ("Both deoxyribonucleases (DNases) and restriction enzymes are endonucleases") is wrong.
For a more complete table have a look at Molecular Biology of Nucleases, page 18.
- Lehninger, A., Nelson, D. and Cox, M. (2000). Principles of biochemistry. New York: Worth Publishers.
- Mishra, N. (1995). Molecular biology of nucleases. Boca Raton [u.a.]: CRC Press.