It might be pedantic but according to Wikipedia the CGI awards a PsyD rather than a PhD: https://en.wikipedia.org/wiki/California_Graduate_Institute

This Wiki page has a little more about the differences between the two: https://en.wikipedia.org/wiki/Doctor_of_Psychology

It seems like the PsyD has more emphasis on clinical practise and (one supposes) less on theoretical research.

Schools may usually issue one, but sometimes issue the other.

Schools also sometimes change which they issue.