When you plug your phone into your car stereo, you are probably using a 3-conductor plug (handles stereo). Look at the end of the plug, if you see two painted indented stripes, it means the plug is separated into three different metal contacts (with the stripes between, I believe they are divided into right speaker, left speaker and either a neutral or power--I'm not an electronics whiz). For phones, it expects a 4-conductor, or a plug with three painted indented stripes (the fourth being the microphone).
The phone only knows that something is plugged in. It is expecting the microphone and two speakers, instead it is only presented with the two speakers.
My older phone, the MotoQ, used a 2.5mm jack, and when I'd plug regular headphones or stereo jack into it, the connections were weird. One half of my headphones would work, and the phone would immediately freak out thinking it was getting some voice command. In a sense, it turned one of the headphone speakers into a microphone (they don't work well like that). It's all on how it where it takes the input (I think this is standardized--http://en.wikipedia.org/wiki/TRS_connector).
I'm betting the droid is doing the same, and no app should be able to distinguish since it's purely hardware-related. For my older phone it took a 2.5mm 4-conductor to 3.5mm 3-conductor converter to get it to work on my car stereos or normal headphones. I believe what we need is a 3.5mm 4-conductor to 3.5 (or whatever) 3-conductor converter.
I was just at Radio Shack yesterday and I couldn't find one.
Without the converter you'll need to unplug the cable to use the phone for a call.