Both are Local Services Ads badges earned through background/license checks. Google GUARANTEED covers home services (plumbers, electricians, HVAC) and backs consumer jobs with a money-back guarantee from Google. Google SCREENED covers professional services (law, financial planning, real estate). Vetting badge, no monetary guarantee.
Either way the commercial mechanics are the LSA model: you pay per lead rather than per click, rank partly on reviews and responsiveness, and can dispute junk leads.
Which you can get isn't a choice. It follows your category. The real decision is whether LSA economics beat your search-ads cost per lead, which only running both for a month answers.