Need to make MP4s with AVC codec not H.264

[helicoptersoup]

I am working on a video project where I need to create mp4 files that say AVC codec in the file properties instead of H.264. My understanding is that AVC and H.264 are the same thing, but videos that say H.264 in the video properties are not working with this proprietary video software our company is using. Whenever I create mp4s in Final Cut Pro, Quicktime, or MPEG Streamclip and then view the info of the file within QT, it says the files are H.264 format. However, when I use Handbrake to make a H.264 mp4, QT says that the file is a JVT/AVC Coding format. This handbrake file works great in our program, but the problem is that I have to compress it once to get into Handbrake and then again to get the file I want. Is there anyway to get a JVT/AVC Coding format file out of Final Cut Pro, Quicktime, or MPEG Streamclip. Sorry if this doesn't make sense and feel free to ask me to clarify anything. Thanks for the help!