Hi Pakistan,
So in January 1892 Argentina was facing possible war with Chile. Knowing it would still be some time before their Mauser 1891 models were delivered they needed a few rifles "right away" and so ordered 5000 Commission 1888 rifles ("Gewehr Model 1888") in the German caliber Mauser 8mm (7.92mm), a different caliber from the 7.65 they would soon be acquiring.
The rifles were manufactured by Ludwig Loewe & Cie for 81.50 Francs each.
These rifles were never issued in an effort to prevent mix-ups with ammunition. Then when the M1891's arrived the entire lot of 5000 was sold to Peru (or Ecuador) at auction on January 19, 1892.
So if you find a Commission Model 1888 in Argentina, it is likely to have arrived being carried in by German immigrants moving to Argentina after WWI (over 425,000 were made by Ludwig Loewe alone), and nearly 100% not likely to be the ones actually bought by Argentina.
By the way you called this rifle a Commission 1889, which there is no such thing - I assume you meant 1888.
Also by the way you asked for info on usage - well they bought some, but never used them, and then civilians brought in perhaps some civilian ones, but they would also never have been "used" by Argentina officially / militarily in any way... so to answer your exact question, there would be zero Argentina usage.
As far as telling these 5000 rifles from the other hundreds of thousands made, there is this cryptic paragraph from Colin Webster's book, which I quote exactly:
"While the rifles purchased by Argentina did not have any national marks to identify them as such, neither did they have any of the marks associated with the modifications made to virtually all European pieces between 1891 and 1905. In this sense it is easy to identify those that were not purchased by Argentina. The Model 1888 had serial numbers stamped on the left side of the receiver ring, left side of the barrel, near the receiver ring, at the base of the bolt handle, on the triggerguard and on the buttplate. All of these carry inspection stamps as well. Just like the Mauser 71, the Model '88 has its test firing and final acceptance stamps on the right side of the receiver ring and on the stock behind the triggerguard. The last two digits were also stamped on the cocking piece, safety lever, and nut. In some examples these two digits and the inspector's acceptance stamp have been found on every part of the bolt. The rings, screws and sight components have also been consistently found to have these two last digits and the inspection marks as well. The crossbolt typically has an inspection stamp."
Ok, but i can find nowhere, what the serial number ranges for these 5000 rifles are, or what the acceptance marks look like. I did find that they are NOT the markings found on the M1891 rifles, as they hadn't been developed yet.
There is a picture of the top ring of one of these rifles with serial number 2407, so perhaps they were numbers 1 to 5000. But in the picture it is too blurry to see the markings well. You can see 2407 twice on the left side of the ring (which would appear horizontal if you were looking at the left side), 3 unreadable markings on the right side, which would be horizontal if you were looking at the rifle from the right side (the bolt side), and also markings you see looking down on the topring that are an "S" (for the S type bullet they took), then a small crest, and them some words below that I can't read.
The specs of this rifle are in the book. They are:
Length 1250 mm
Length with Bayonet 1635 mm
Weight 4.100 kg
Barrel Length 740 mm
Rifling 4-groove, right hand
Sights: Leaf and V notch / inverted V notch, ranged 250-2,050 meters
But again these would be the same specs as hundreds of thousands of other rifles.
Regarding your other question on FN 1889 rifles. FN didn't make any 1889 rifles for Argentina. It appears that from 1892 to 1901, only Mauser Model 1891 or 1892 rifles were purchased (rifle and carbines), and those were made by two companies... Ludwig Loewe or Deutsche Waffen und Munitionsfabrik.
On page 237 of Webster's book, there is this note about FN:
"FN, originally Fabrique Nationale D'Armes de Guerre and later changed to Fabrique Nationale, is located in Herstal, in the Belgian province of Liege. This company, in which Ludwig Loewe & Cie and later Deutsche Waffen und Munitionsfabriken, owned 50% of the stock, was formed in 1889 with the purpose of fulfilling a contract for 200,000 Model 1889 Mauser rifles. Belgian law required the weapons be manufactured locally. Following the completion of the Belgian army's Model 1889 it obtained contracts from Brazil for 50,000 model 1894 rifles. Loewe and Mauser were precluded from supplying other South American countries under the terms of their 1891 contract with Argentina. Another 100,000 Brazilian Model 1894 rifles were later purchased by Uruguay, Colombia and China..."
So if you have an FN 1889, then it is Belgian, and as far as I know, never officially used or acquired by Argentina.
My best,
Kevin