no need for a discount if there's a cap. Discount is nice if you don't want to try and set a cap/price, but if you're OK setting a cap then it effectively grants a discount
I think Daniel was working off of a different understanding of 'discount.' I think he meant a discount off of the price of the next round (Series A). If the Series A is $30M pre but you set a valuation cap on the safe of $20M post, you are getting a 'discount' on the conversion of the safe in the Series A (because it is lower than $30M pre).
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.
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.