Back to the question , Mjaddara for me is the one with rice (mich mat7ouneh). The other one, (il mat7ouneh) , I know it but we are not used to it, so I can't qualify it by any name (my friends from the mountain, call it mjaddara, so ...)
In cook books it's called mdardara. We call it mjaddara. The story goes as such: In the past, men found that 'mdardara' sounded mna3na3a, while the one spelled with a 'j' and double 'd' sounded more rough. To prove their manhood and create a reputation, they started using it in front of other men as they shouted onto their wives with '3melilna sa7n mJaDDaRa ya mara!'. The tradition was passed from father to son, and hence all still call it mjaddara now.
Whether mjaddara or mdardara, it's a horrible dish. Possibly the worst after fatty meat.