My fiancée is an INFJ and I'm an INTJ. We work incredibly well together. Here is a very simplified difference between the two of us: (This may not be the same for everyone but maybe the general idea of it)
We are generally the same (besides the whole "colder" and "gentler" thing) but here is where it breaks up. She, the INFJ, wants to "fix" the world; to "fix" society and all the people in the world because she cares. I, the INTJ, want to fix the "materialistic" things for efficiency; to provide a better system for all or even myself because I also care but because we are impersonal, it can come off like we don't care.
We both want to "fix" things. INFJ wants to fix the community. INTJ wants to fix everything else around it FOR the community whether it be a company, group of friends, or personal circle of people. Because INTJ's are impersonal, they skip the whole "people matter" part. Because INFJ's are so personal, they skip the whole "how it works" and focus on "who it works for".
Just like my signature says, "He who has a WHY can endure any HOW". The INFJ is the "WHY". and the INTJ is the "HOW".