The terms are virtually interchangeable. They can call themselves whatever they want.
Back in the days of truth in business a distributor would have an assigned territory and then sell to wholesalers in that territory, but with the internet everyone is everything. Don't worry about the name or title, look at the cost.
An "authorized distributor" is a nation wide distributor authorized by the brand owner to distribute there products.There's also regional distributors which have a specific sales territory by the brand owner.
A wholesaler is usually further down the supply chain,they may be buying from multiple sources.Examples: distributors,importers,closeout and liquidator companies.
Most "name brand" goods have only a few "authorized distributors" for the brand.