I just saw an ad in my local newspaper for a "vintage black sears featherweight with carrying case and attachments" for $400. If it's not a Singer it's not a featherweight, right? Should I call or go check it out?

Right.
But, maybe the person used the word Sears by mistake. I would at least check it out, although 400 is a lot for a genuine FW.

Singer Featherweights were made between 1933 and 1964 and weigh about 11 lbs. Model 221. Check this site for just about all you would want to know about them. http://www.planetpatchwork.com/fweight.htm

There a more rare free arm Model 222 along with the 221, but those are the only FWs. Singer made at least two 3/4 size machines - the 99 and the 128, but, believe me, they are not light. My 128 could double as a boat anchor.