A PhD is commonly done after a master's degree (can be done after a bachelor's degree). This type of degree can take 5-7 years to complete. This degree is research-intensive with a dissertation/thesis requirement.
A PsyD is very similar to a PhD. The main difference is that a PsyD is less research-intensive. PsyDs focus on clinical work and practice.
LinkedIn lists a broad selection of jobs, includes police & corrections but also unconventional CJ jobs like gun vault operators, anti-shoplifting specialists, social service case managers, behavioral hospital supervisors, etc.