Standard deal does not have a discount?
Example: raising 1M at 10M cap, 20% discount.
Scenario 1: next priced round at number below 10M - the cap doesn't apply, the discount does.
Scenario 2: next priced round at number between 10M and 12M - the cap doesn't apply, the discount does.
Scenario 3: next priced round at more than 12M - cap applies, discount doesn't.
In short, either cap OR discount are applied, whatever is the most beneficial to the investor.
You're right though that there's a flavor of safes that contain both a discount and a valuation cap, and the investor gets the benefit of whichever approach results in more shares, and your explanation is good.