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It's a bit nebulous, but as a rule high-annual-fee/interest rate rewards cards are built around this model; the higher the annual fee, the less interest income a bank expects to earn.

Issuers tend to specialize, too. For instance, banks like Barclays, Chase and Amex only (intentionally) target prime customers. Chase has been known to fire customers that suddenly start carrying significant balances on their cards, for instance.

On the other hand, banks like Capital One and Credit One explicitly target subprime customers and make the vast majority of their income from interest. Whereas Amex makes 90% of their card income from annual fees/interchange, for C1 it's more like 90% interest/10% interchange. Chase is like 65/35 Interchange/interest, for comparison.

For Amex, the simplest rule is that any card named after a color (Amex Gold, Amex Green, Amex Platinum etc) doesn't charge interest.

Oh - and the Amex charge cards don't actually have no limit. They do have a line, it's just hidden (and somewhat larger than most credit limits). Amex actually has a 'check my spending power' tool on their website where you can plug in a hypothetical purchase and it'll tell you if they would (hypothetically) approve it.