Short answer: No, but they're remarkably similar. Royal Gourmet is owned by Royal Distributors Inc. and sells direct-to-consumer through Amazon, Walmart, and Home Depot. Outdoor Gourmet is Academy Sports + Outdoors' own private label brand, sold exclusively at Academy stores and Academy.com. Both are budget-tier outdoor cookers manufactured at Asian factories, and the factories sometimes overlap — but the brands have separate parent companies, separate model lines, separate warranties, and separate parts ecosystems.
Why this matters for buyers: Don't assume parts cross-fit between the two brands. They sometimes do (when both happen to source from the same factory) but often don't (when each brand uses a different supplier). Don't assume the warranties are equivalent — Royal Gourmet's 1-year warranty service runs through Royal Distributors; Outdoor Gourmet's runs through Academy Sports' returns policy, which is generally faster and more flexible. Don't assume the model numbers translate — there's no 1:1 mapping between Royal Gourmet's GA5404S and Outdoor Gourmet's similar-spec 4-burner; they're different SKUs.
Which is better depends on what you're optimizing for. Royal Gourmet has the deeper offset smoker line (the CC1830S has no Outdoor Gourmet equivalent at the same price) and broader Amazon parts availability. Outdoor Gourmet has Academy Sports' return policy advantage, in-store pickup, and the Triton griddle combo line that Royal Gourmet doesn't directly mirror.
The honest framing: these are two budget grill brands competing for the same shopper. If you live near an Academy Sports, Outdoor Gourmet is more convenient. If you shop online primarily, Royal Gourmet has the broader product line and better parts ecosystem. Neither is meaningfully "better" than the other in cooking performance — both produce comparable food at comparable prices.