If that is a B-78 it is a re-barrel.  The B-78 uses coil springs and has a rebounding hammer.  The B-78 looks like a highwall on the outside but is quite different inside.
I once took one apart to do a trigger job and ran into trouble.  I contacted a rep for Browning and he told me to not take it apart because even the techs at the plant had trouble with the.  When you pull the breach block down there are three detent springs with small steel ball that go boing in three different directions. I think you have to be Japanese to re-assemble them.  I did get the trigger done but without the proper jig to compress the detent springs it requires more fingers that one man has.  I cant remember for sure but think if you drop the breach block and look at it from the bottom with a Browning you should see dual coil springs.  They are great guns very strong actions but a bugger to work on.
When I was a young man laid off from Alaska timber falling in winter I hunted coyotes in Montana all winter.  My preferred rifle was a B-78 browning in 6mm Rem.  The reason was that it came with a long 26 inch barrel the got all the velocity the cartridge was capable of but even so had a shorter over all length that a bolt action with a 24 inch barrel.  This puts the balance point closer to the shooter so is steadier for off hand shooting. In hunting fur for money you have to take the shots as they come and in coyote hunting about half your shots are off hand.

Front sling mount is part of the barrel, not added . I do see the dual springs when lever is lowered. I have several 1885’s (Browning and Winchester) but realized something was different. Will Browning confirm serial number with a call or is there a process? Anyone know if Browning ever chamber B78 in 338?

"No identifying marks anywhere on barrel or receiver".

The B-78 was never offered in 338 WinMag.

It's been re-barreled.

A chamber cast will tell the tale.

The B-78 Browning came in 45-70, 30-06,  7mm Rem mag, 25-06, 6mm Rem, and 22-250.  Possibly 243 but I have never seen one.
Standard barrel length was 26 inch and came in the heavy round or light octagon configuration.  The 45-70 was an exception that only came in octagon.  The 45-70 was also different in that it came with a crescent steel butt plate.
My preference was the heavy round barrel.  As I said earlier my preferred caliber for coyotes was the 6mm Rem but I did have another one in 22-250 as a back up rifle. In those days I hunted every day from daylight till dark. It wasn't something I did for kicks it was something I did in the winter months to make a living.  Back then early 80's coyotes paid good money.

Hoping this is a custom build. Stock is also different from any I have or have seen. Browning confirmed the serial number today , 1973 issue date, but has no info on original caliber. Has nice Browning bases and rings and mounted a Leupold 3x9x40 I had stuck back from something else. Feel sure on caliber since the previous owner sent me his remaining hornady and federal ammo he had used. If I can figure out how to reduce size of pictures I’ll post.

Photo of stock.

My setup

I too fought a B78.i swear I needed 5 hands to get it together. I gave up and my gunsmith had it together in 5 minutes. He had some dummy pins and a tool IIRC .it was 30 years ago so I don't remember what he did that looked so easy.

For hunting elk, and the larger North American big game, the 338 is hard to beat. If one can handle the recoil!