I am confused between these 2 

Invoice Id and Payment Id are different .

Invoice id's are used to track invoices, whose control policy might be different. But payments Id will only show yoy the payments happened . It helps you track payments . 

Let's assume two scenarios 

Scenario one 1 : your customer wanted to pay with different methods for a single invoice ( may be half with bank and other half with cash ) .so now if you register payment with both method , 2 payments  will be created linked with single invoice . Now these payment ids help you track the payments.

Scenario two  : you have added different products and you  delivered  half and other half will be delivered later . now you can create two invoices one for delivered id other for the non delivered products in this case its difficult to track by payments id but easier with invoices id .