If you mean the previous claim of there being an Alpha Centauri Bb planet, later retracted, then this new finding involves a completely different star, not just a different period.

This is around Proxima Centauri, the previous one was around Alpha Centauri B. Proxima is a really really small red dwarf, just 12.3% the mass of sun, while Alpha Centauri B is a K-type star, ie somewhat smaller than sun but not that much; around 90% of Sun's mass (And there's also Alpha Centauri A, 10% more massive than the sun). We're not even 100% sure that Proxima is part of the Alpha Centauri system, though I gather it's considered highly likely - it's pretty distant from the Alpha Centauri system, some 15 000 AU (1 AU = distance between Sun and Earth), almost a quarter of a light year.