I thought they are different too, but actually I think there's a bug. I use DNN 06.02.05 (24) and Form and List 5.1.3, but i test this with other versions too (inluding DNN4.9 + UTD).

What I've tried:
1. I go to Manage Form and List -> Settings -> Permissions tab
2. On a test UserRole called 'TestRole' i apply the following permissions:
2.1. 'View Module', 'Edit Record', 'Delete Record', 'Create Record/ Submit Form'. Then i don't see the 'Manage' button of FnL module when trying to login with the user have 'TestRole'
2.2. 'View Module', 'Edit Module', 'Edit Record', 'Delete Record', 'Create Record/ Submit Form' - this way i see Manage button and i have 'Add new record' and also i have the links: the links "Form And List Configuration" and "Delete All Records"

3. If i try to put 'Edit Module' to 'Registered Users' and 'View Module', 'Edit Record', 'Delete Record', 'Create Record/ Submit Form' to 'TestRole' then again i have the same options in 2.2.

What should i do?

Still not completely solved, but what i did:
1. I installed DNN 7 and installed later FnL 6.1 and all works good - as it should be (when you have 'Create Record/ Submit Form' and allows you to 'Add New Record' without seeing the links "Form And List Configuration" and "Delete All Records".
2. On my other DNN 6.2.5 instance, i updated to FnL 6.1. but still it acts wrongly as described in my previous post.