Payment Initiation Service Provider will be allowed to communicate securely with the Payment Service User's Account Servicing Payment Service Provider (ie Bank) which hold the Transaction Account and seek information required for payment initiation.
Payment Initiation Service Provider will use software to link the merchant’s website or Application (think Open Banking API) with the Payment Service User's Account Servicing Payment Service Provider for initiating payments.
P2P transfer and bill payment are Payment Initiation Service Provider services we are likely to see when PSD2 is implemented.