I got a flu shot. They were out of the one that goes into the muscle, they gave me the one under the skin. Is there a difference in efficacy?

Possibly. Influenza vaccination, with bivalent split virus vaccine (a/new jersey/76 and a/victoria/75), compared the immunogenicity when vaccine was given by the subcutaneous and intradermal routes. For the a/victoria vaccine, the immunogenicity given intradermally seemed superior. For a/victoria/75 there was no difference. These differences, if real, are probably not clinically significant.