App Protection: Custom app vs Partner app

Is there any functional difference in using an app protection policy to manage a public partner app versus a custom application?

We have an app vendor that says they wrapped their app with the SDK but it is not on the partner list so we cannot pick it from the public app list. Which leaves us with the custom app option. Is the functionality the same? Will it show up on the app protection report, work with conditional access policies, other Microsoft solutions, etc.?

Thank you - 

Jessie