Deflate is just the compression algorithm. GZip is actually a format.
If you use the GZipStream to compress a file (and save it with the extension .gz), the result can actually be opened by archivers such as WinZip or the gzip tool. If you compress with a DeflateStream, those tools won’t recognize the file.
If the compressed file is designed to be opened by these tools, then it is essential to use GZipStream instead of DeflateStream.
I would also consider it essential if you’re transferring a large amount of data over an unreliable medium (i.e. an internet connection) and not using an error-correcting protocol such as TCP/IP. For example, you might be transmitting over a serial port, raw socket, or UDP. In this case, you would definitely want the CRC information that is embedded in the GZip format in order to ensure that the data is correct.