Yes Pampers does make Luvs Diapers.
Both Pampers diapers and Luvs Diapers are made by the same company which is Procter and Gamble.
Pampers was the first brand of diaper that was made by Procter and Gamble and then Pampers or Procter and Gamble started making a cheaper but good quality version of their diapers which they called Luvs diapers.
So while Pampers and Luvs diapers are differently made diapers they are both made by the same exact company who makes Pampers and Luvs diapers.
Luvs diapers are great and hold up just as well as Pampers but at a cheaper price than Pampers.
But some kids may be allergic to certain things in the diapers so you may need to try either Pampers or Luvs or a different brand.
Both pampers diapers and Luvs diapers used to have regular tapes on them and were all a thick plastic backed diaper.
When I was a baby I wore those plastic backed Pampers diapers that were thick.
I have some pictures of me when I was 2 years old wearing those thicker Pampers diapers.