Thanks, EN, I now understand the context.
Hanson was comparing the fowling pieces the Hudson Bay Co. was trading to the Indians in the late 1600s to the military musket of the day. The "common musket" he referred to was a military musket, but not the Brown Bess. The Brown Bess had not been developed and adopted until later in the early part of the 18th century.
In the next sentence after the one you quoted, he continues the comparison, "Even in Queen Anne's time [1702-1714] the colonial fusil was but a full-stocked musket of lighter caliber than the regular military piece."
You ask, "Also they mention the 'All purpose musket'. Art [sic] they the same?" I assume you are asking is the "common musket" and the "all purpose musket" the same. In this instance, I think Hanson is referring to the gun shown in Plate IA, 1 and in Plate IB as the "all purpose musket". If so, the answer is no, they are not the same. The gun in Plate IA, 1 is later (early 1700s) than the "common musket" of the 17th century.
Hanson published The Northwest Gun in 1955. It was a pioneering effort in the study of Indian trade guns. There wasn't a lot known about the early trade guns and Hanson was making educated guesses and speculating on what the trade guns of the later part of the 17th century and first half of the 18th century looked like. There was very little archeological information prior to 1955 and no recognized surviving samples of these early trade guns. He was guessing that they looked similar to known samples of 17th century and early 18th century English military muskets. He was trying to make the case that the Northwest trade gun was developed from English military muskets.
It turns out he was pretty much right about the mid- to late-17th century trade guns. But not so lucky concerning the trade guns of the first half of the 18th century and about how the Northwest trade gun came to be. It wasn't until the next decade that T. M. Hamilton had studied extensive archeological artifacts from public and private collections and categorized them into Types, that Hamilton and other collectors began to realize that Hamilton's Type G trade gun was the most prevalent trade gun pattern in much of the first half of the 18th century and was the precursor to the Northwest trade gun.
The trade guns of the 18th century, with the exception of the Northwest gun, were simply less expensive English fowling pieces. The fowling pieces themselves had adopted characteristics of the military muskets such as the "hand-rail" wrist and butt stock, but they were slimmer and lighter with smaller bores than the military muskets of the period.
The Hudson Bay Co. developed the classic Northwest trade gun over a period of a few years in the middle of the 18th century including the large bow trigger guard and the particular cast dragon sideplate. It continued the flat sheet brass butt plate, ribbed ramrod thimbles, and tang screw coming up from below from the Type G and even earlier guns such as the Club Butt.
The way to view it now is that the English military musket influenced the English fowler which in its most basic and inexpensive form was traded to the Indians. The Northwest gun was a specialized trade gun developed by the HBC that had no civilian or military counterpart. It came from the minds and hands of the View Masters that worked for the HBC and evolved from trade guns that came before it.