The alpha wolves are indeed the mama and papa wolves. The terms are synonymous, although for the most part, you are correct, the term "breeding pair" is more commonly used than alpha these days. As you'd see if you read my linked story about wolves called "I feel sorry for alphas" I mention that wolves were originally studied in captivity, where animals from various packs were lumped together which caused them to fight for status. This is a part of where the idea of a tough, belligerent alpha comes from, but once they started being studied in the wild, that whole idea was realized to be the result of human intervention and not natural wolf behavior at all.

https://medium.com/inside-of-elle-beau/i-feel-sorry-for-alphas-5edc35984034

I"n the wild, an Alpha wolf is the daddy of the pack. He’s the male part of the sole breeding pair and together with his mate, they care for and raise their cubs. In fact, now that researchers have actually bothered to study wild packs rather than groups of unrelated wolves in captivity (which is where the concept of the tough, aggressive, take no shit Alpha who has fought his way to the top originated back in the 1940s), the term now most commonly used to describe an “Alpha male” is simply “breeding male.” The pack consists of a breeding pair and their cubs from the past 1–3 years."