That was the SW380, a little striker-fired pistol in the Sigma series. It had a 3" barrel, weighed a claimed 14 ounces empty, and had a six shot magazine that was released by squeezing two large tabs, one on either side, like it was the battery pack in a power tool. It was a straight-blowback pistol with a zinc alloy slide and, as a result, had a beastly heavy recoil spring that made cycling the slide a difficult proposition for those without a lot of grip strength.
The slide was finished with black paint that chipped easily. The gun was built to a price and looked it. Reliability was poor and the guns had a notoriously short lifespan, being cynically designed with an eye toward the fact that the typical purchaser probably wouldn't shoot them much. Production ran for only a year or two and then Smith & Wesson dropped the .380 cartridge from its catalog for over another dozen years before releasing the Bodyguard 380 (sometimes referred to as the BG380) in 2010.
Also unlike the earlier Sigma, the Bodyguard is a hammer-fired pistol. Since the slide has to overcome not only the dual concentric recoil springs under the barrel, but also force the hammer back against the hammer spring, the slide can be much slimmer and lighter than the one on the earlier striker-fired blowback gun. Like the larger pistols in the M&P series, the slide is Melonite-finished stainless steel. The BG380 weighs 14.7 ounces with 6+1 Hornady Critical Defense .380 FTX rounds aboard.
Most of the little .380s in this class, like the Kel-Tec P3AT and the original Ruger LCP, are only quasi-double-action. The hammer spring is cocked by the action of the slide and pulling the trigger just causes the the hammer to move, sort of like the old Para-Ordnance LDA or HK's LEM. The Bodyguard 380, on the other hand, is a true double-action only, with re-strike capability and all.
Originally all BG380s had an integral laser in the frame, activated by the gray button in front of the trigger guard. The likelihood of activating this thing when reacting under pressure is about nil, practically speaking and, in 2014, Smith started offering a version without the integral laser.
I bought the pictured pistol new back in 2013 and used it for wintertime coat pocket carry for several years. The slide is not the original one, being fitted with XS Standard Dot night sights. It was a gift from a friend, having originally been on his BG380.
.