How did Peter Hale form the original pack? Did they perform some rite? How does a shape-shifter become the original Alpha? It can not be done by being a True Alpha because... well Peter never was one (sorry Peter). And yet Peter was the original Alpha.
As far as we can tell, a Pack is formed by the simple act of an Alpha gathering other weres to follow them.
Keep in mind, Scott is practically unique in the Teen Wolf world, so we can learn a lot about how packs work in theory from him, but in practice, things for other packs never actually work that way.
In general, packs likely formed long ago, when the werewolf species first appeared. The strongest of those wolves became the Alpha, and the other members of the pack followed them. From then on, the packs remained constant; as one Alpha grew old and weak, another were would kill them and become Alpha. At that point, presumably, the old Alpha's pack would just transfer to the new Alpha. Peter became the Alpha by killing his niece; presumably she became an Alpha by killing a previous one, etc.
But we have seen at least two other packs form "spontaneously" in the show: Scott's pack, and the Alpha Pack.
With the Alpha Pack, Deucalion went around to other pack Alphas and showed them a way to make themselves stronger, by
killing their own pack members
As a result, those super-powered Alphas began to follow Deucalion's lead by choice, thus creating a new pack made entirely of Alpha wolves.
In Scott's case, he wasn't an Alpha at first. However, his sheer strength of character convinced other weres, including non-wolf weres, that he was someone who deserved to be their leader. They naturally fell into the habit of following his lead, and as they did so, Scott started to become a "True" Alpha.
I think we can infer from this process, and based on the name they use for it, that the original packs all had True Alpha's as their leaders. The subsequent Alphas killed the original True Alpha pack leaders, but couldn't become True Alphas that way, so the "regular" Alpha was born.
Sorry man, this show is famous for confusing itself regarding mythology, I don't think you'll be getting any complete answers.
That being said...
I'm not sure what you mean by "original" Alpha, but Peter became Alpha by killing the previous Alpha (his niece).
"True" alpha simply means Scott didn't have to kill anyone to become an Alpha, no other significance to my knowledge.