How does recompense differ from punishment in the Qur'an

[miracle114]

Salaam all,
I found this Ayat

(Sahih International)
What would Allah do with your punishment if you are grateful and believe? And ever is Allah Appreciative and Knowing.

-Surah An-Nisa', Ayah 147

How can one differentiate between a recompense and a punishment and hence a test.
For someone who committed major sins before a becoming a believer, how does Allah deal with them?

Kind regards
God Bless all