Full mouth debridement vs deep cleaning, what's the difference?

Big difference. Deep cleaning is scaling and root planning, which is treatment for gum disease with pockets deeper than 3-4mm. It takes more than one visit and costs considerably more. When indicated, it is absolutely necessary. Full mouth debridement is usually when someone hasn't had a cleaning in a while and during the initial hygiene visit, the tartar above the gum line is removed. Srp may be required next.