The distinction between "basic" and "premium" cable is much muddier these days, because what is classically "basic" is no longer a single pacakage but a bunch of tiers, and what is classically "premium" is no longer sold on a channel-by-channel basis (e.g., HBO used to be one channel, paid separately) but in its own packages (e.g., all HBO, Cinemax, and Starz channels together as one package) by cable providers.

But, yes, "premium cable" channels are things like HBO, not things like BBC America, even if the latter is only available on the top 3 of 7 tiers from a given provider.