Both specialists deal with oral health, but a periodontist is a more highly qualified specialist.
A hygienist is a mid-level medical professional (junior specialist, junior bachelor). Has permission to perform routine professional dental hygiene, teach patients hygiene, and perform simple procedures (for example, fluoridation of teeth). Can detect signs of inflammation, but does not have the right to perform diagnostics (diagnosis) and treatment.
A periodontist is a doctor with a higher education (master's degree), completed internship, and specialization in periodontology. A periodontist has a deep understanding of anatomy, diseases, and treatment protocols. Has the right to perform diagnostics, prescribe and administer treatment, write prescriptions, and perform surgical interventions (gum plastic surgery, curettage, scaling, flap surgeries, etc.).