I bought a le Potato and an emmc module.  The module fits fine on my odroid.  The le Potato has the same connector gender as the emmc module however and cannot be connected.  Do emmc modules come sometimes with male and sometimes female connectors?

Did you buy the eMMC with the Le Potato?  I have no idea if it is compatible with other vendor parts, I don't think there's any expectation that it would be.

No I didn't buy it with the potato.  I just assumed emmc was standard like an sd card.

Afraid not, in fact even if it physically fit, and electrically worked, it's possible it could have the wrong partition layout, which cannot be changed.  Remember these are intended to be soldered directly to the application, the socketing is just a nice SBC thing for the most part