Neither of those seem true, in any meaningful sense. The distinct terms for which direction it faces were only applied retroactively by Western scholars. Suawastika or swavastika still means the same thing, which is basically “auspicious emblem”.
Nazi flags were stitched through so that the emblem would be facing either direction depending upon one’s orientation to it. So these would be both swastikas and swavastikas. I have seen the same thing done on the tails of airplanes as well.
Neither Dharmic people nor Nazis use either version exclusively, so as a rule-of-thumb to discern between groups, I find it ineffective.
I do find the different uses in Dharmic disciplines interesting, but that gets esoteric rather quickly.
