Most of the focus of the Western fur trade was beaver. However, other furs were collected, through trapping, trading and hunting.
Let's look at a few references to collecting other furs:

From W.A. Ferris:
During these rambles we sometimes saw an animal resembling an otter, in size, shape and color,
called a pekan or fisher; but for want of a dog to tree them, did not shoot any. We killed several
martins, and saw the traces of a large animal of the cat kind, supposed to be a lynx.

From Washington Irving:
The export trade of furs from the United States is chiefly to London. Some quantities have been
sent to Canton, and some few to Hamburg; and an increasing export trade in beaver, otter, nutria,
and vicunia [relative to alpaca] wool, prepared for the hatter’s use, is carried on in Mexico.

From John C. Luttig:
Thursday the 1st of October, at Sunrise we had to cross a band of Sioux, accompanied by Nez
Corbain and another Chief called Boite about 40 in Number they traded and returned at noon
satisfied, in the afternoon 7 Men started up the River with the Mackina Boat to hunt Buffaloe, and
Immel came home with 15 Beaver 1 Otter and 2 Muskrats, wind blew very hard from N.W. and
the Boat returned.

our hunters arrived with Meat of 2 Cows.
They had Killed 7 and caught 20 Beaver 1 Otter 2 Muskrats and Killed 2 Wolves.

From William Kittson:
Two more of the absent men have joined us. The beaver got this day amount to 133 and 1 otter. We
have now completed our first thousand.
Late last night 7 of the 9 absent trappers made their appearance; only 93
beaver and 9 otter.

From James O. Pattie:
We were all weak and emaciated. But I was
young and able to bear hardships. My heart only ached for my poor father who was reduced
to a mere skeleton. We moved on slowly and painfully, until evening, when we encamped. On my
return from setting our two traps, I killed a buzzard, which, disagreeable as it was, we cooked for
supper. In the morning of the 18th, I found one of the traps had caught an otter.
This served for breakfast and supper.

Lost Greenhorn, by A.J. Miller.

Buzzard and otter? They musta been starving.

Here's the few lines before that quote:

The miserable condition of our
company may be imagined, when seven hungry men, who had not eaten a full meal for ten days,
were all obliged to breakfast on this nauseous bird. We were all weak and emaciated.

No meal for 10 days. At that point I sure would pretty much anything I could get my hands on.

From Washington Irving:
The export trade of furs from the United States is chiefly to London. Some quantities have been
sent to Canton, and some few to Hamburg; and an increasing export trade in beaver, otter, nutria,
and vicunia [relative to alpaca] wool, prepared for the hatter’s use, is carried on in Mexico.

Was Irving an actual trapper or was this taken from his book "Astoria"?

From his Astoria book.

The annual reports of Hudson Bay company Columbia district listed many other furs sailing out of Ft Vancouver besides beaver.

man, we don't know hunger, 10 days without food,

Here's a list of furs purchased by the Northwest Company from the Astorians, during the takeover of the operations.
Valued is what the NW Company paid the Astorians, worth is what the NW Company would sell them for on the market.
Beaver parchment is stretched and dried beaver.
Coat beaver are older tanned beaver.

The following estimate has been made of the articles on hand, and the prices:
17,705 lbs. beaver parchment, valued at $2.00 worth $5.00
465 old coat beaver, valued at 1.66 worth 3.50
907 land otter, valued at .50 worth 5.00
68 sea-otter, valued at 12.00 worth 45 to 60.00
30 sea-otter, valued at 5.00 worth 25.00
Nothing was allowed for
179 mink skins, worth each .40
22 raccoon, worth each .40
28 lynx, worth each 2.00
18 fox, worth each 1.00
106 fox, worth each 1.50
71 black bear, worth each 4.00
16 grizzly bear, worth each 10.00

Cool stories, Patties story reminded me of trip to Canada where I learned about starving vs hungry.

My brother and I took a buddy to Canada 30 years ago. The buddy was a Polish immigrant. We went out fishing early one morning. Got to be around 11:00 my hang over was fading so I said, “let’s start working our way back, I’m starving”. My Polish buddy said “Shawn, did you eat anything yesterday?” I said “Yes, you were sitting right next to me.” He said, “Exactly, starving, pfft! your not even hungry yet.”

Since then I don’t think I’ve ever described my condition as starving. Hungry, peckish, hollow, but never starving.

I've never truly been starving. Rarely even truly hungry. My brain may have thought I was hungry, but my body not so much.

A trick I use now, to keep my weight down, is ask myself, am I hungry enough to eat a can of plain sardines?

Good stuff. Did that come from Irving?

BP, yes, that's from his Astoria book.

In Alfred Seton's narrative "Astorian Adventure" he claims that NW company paid fairly for the fur and supplies when they took over. I think Astor had a totally different opinion when he found out what had transpired. Seton was the lone American left in Astor's group on the Columbia. I think all the rest were Canadians. Irving relied heavily on Astor's take on things as he was the one sponsoring the book.

The following is from Seton's Adventures. It doesn't sound like he was particularly happy with the
outcome of the purchase. Other than he was happy there was no military action involved in the takeover.

at length the price
of the goods and furs in the factory was agreed upon, and the bargain was signed by both parties
on the 23d of October. The gentlemen of the Northwest Company took possession of Astoria,
agreeing to pay the servants of the Pacific Fur Company (the name which had been chosen by Mr.
Astor), the arrears of their wages, to be deducted from the price of the goods which we delivered,
to supply them with provisions, and give a free passage to those who wished to return to Canada
over land. The American colors were hauled down from the factory, and the British run up, to the
no small chagrin and mortification of those who were American citizens.
It was thus, that after having passed the seas, and suffered all sorts of fatigues and privations, I lost
in a moment all my hopes of fortune.

This section from Seton makes it sound like he agreed that Astor got shafted:

D. M’Dougall, as a reward for betraying the trust reposed in him by Mr. Astor, was made a Partner
of the Northwest Company, crossed the mountains, and died a miserable death at Bas de la
Rivière , Winipeg.