Sterling silver is 92.5% fine silver and 7.5% copper. The copper is what causes all sterling silver to tarnish over time from exposure to sulfides in the air, perspiration, etc. Argentium is 92.5% fine silver, with the remaining 7.5% being an alloy called germanium and then less copper. Argentium® Sterling silver is a registered trademark.
There are a number of differences for a silversmith working with one or the other. Sterling silver often develops firescale during the soldering process - which has to be sanded away. Argentium does not develop firescale and actually fuses to itself. There are also some annealing and hardening differences between the two. As a silversmith, I have to be very organized with my stock. If a tag label falls off a coil of wire, or if sheet metal gets mixed up, I'll have a quandary on my hands to sort it out!
But for the buyer, the greatest advantage to a piece of jewelry made from Argentium is that it will often have a more brilliant shine, that is almost tarnish resistant over a long period of time. Additionally, some people with sterling silver allergies can actually tolerate Argentium.
Argentium sterling can be hallmarked .925 or "sterling silver" since Argentium sterling is sterling silver. Special "Argentium" hallmarks have been developed, but the stamps are usually pricey enough to cause a silversmith pause before making such a purchase. In other words, you may not be able to tell which metal your jewelry is made from by the stamp alone.
Bottom Line: The only way to tell the difference between traditional sterling silver and Argentium is through abrasion and/or heat analysis - which would likely ruin the jewelry! Your safest bet is to purchase from a reputable artisan who keeps their silver stock well labeled and organized so they can tell you which product you are buying. Jewelry designs from Argentium are often a little higher priced.