Your hunch re. regionalism is correct.
In most parts of Germany, cream is Sahne, Swiss German uses Rahm, so does Swabia1 and South Bavaria2, Austria calls it Obers.
Now as you probably expected, this is too simple. (Sweet) Cream comes in two varieties: liquid and whipped. And the linguistic Rahm-Sahne-border is not the same for both preparations, at last in SW-Germany. Born and raised with a Swabian dialect, the liquid cream for me is Rahm, if it's whipped, it turns into Sahne - without any qualifier like "Schlag-". Northern Germany distinguishes between Sahne (-> liquid) and Schlagsahne (-> whipped). Likewise for Switzerland (Schlagrahm) and Austria (Schlagobers).
And once you realized that Sahne and Rahm are the same stuff, it becomes clear that a Rahmsoße and a Sahnesoße both indicate a preparation refined with cream. Easy, right?
1 I tried to find details about the distribution in the Atlas der deutschen Alltagssprache, unfortunately without success. Input from other comunity members is very welcome.
2 Altbayern, i.e. Upper Bavaria, Lower Bavaria and the Oberpfalz.