When using PayPal, we DON'T want to collect credit card info!
I've not tried all these options out, but looking at the documentation for Payment Processors (user guide and system administrators guide there is more than one PayPal payment processor. With PayPal Standard all the credit card details are collected on the PayPal site and with PayPal Pro they are collected on your site and transferred by SSL but not kept. There is also PayPal express. I suspect that you maybe using different Payment Processors for your two cases. Certainly worth checking what you have and adding that to the question. I'm not sure what the relevance of Pay Later is having never used that, but I think that's for offline collection of the payment.