The FN Semi Auto 22 (SA 22) that was JMB design was built by FN starting in 1914. Bad timing with WW1 starting. But FN did not call it the Browning SA-22. It was the FN SA-22,,Browning's Patent.
The little rifle was NOT exported to the USA for sale, though some undoubtedly found their way here.
(The same thing happened with FN's little 22 pump rifle of the same period.)
What did happen is an agreement was reached betw FN and Remington Arms to produce a near identical edition at Remington Arms in Illion starting in 1919.
The Model 24 was for USA and North American sales, a market that FN agreed not to enter with the Model FN SA-22.
This type of agreement had been settled upon before in the production and sale of the Remington Model 8 & nearly identical FN Model 1900 rifle.
Browning, Colt and FN had the agreement on the production and sale of a couple of the semi auto pistol designs also.
The Remington 24 was only slightly different from the SA-22. The Bbl TD system being the most noticable. The frames are different in size and there are small changes in the ejector and extractor.
The Model 24 was made till 1935 IIRC. At that time Remington re-did all of their rifles with heftier stocks and a few other small changes in sights, etc.
All of the Model #'s got a '1' added to them.
The 24 became the 241,,,The Model 8 became the 81,,The Model 14 became the 141,,
The 241 was made till 1949 or 1950.
Back to the FN SA-22.
None were imported for commercial sale in the USA till Browning Firearms Co was established in the USA in the mid 1950's.
The FN SA-22 that was made for export and sale in the USA became the 'Browning .22 Semi Auto Rifle' / Made in Belgium by FN.
People always called them Brownings and many thought that they were made by Browning.
(The Model 1910 FN 32 and 380cal pistol was renamed the Browning Model 1955 at that time too and was imported and sold as such.)
So the FN made SA-22 rifle started coming into the USA just a couple years after Remington stopped production of the Model 241.
Everyone was happy I guess in the corporate world of guns. Gentleman's agreements were still alive.
The SA-22 was FN made till about 1974. Since then they had been made in Japan (Miroku ?).
The older FN made guns get a value premium in the collector playground.
The Japanese made version shoots and functions just as well.
Even the Norinco guns work pretty well but are crude in their machining and finishing when comparing. The price reflected that up front so it was no secret.