Are there reliable ways to distinguish anger from fear, be it through body, mind, internally, externally? I've read about some of the differences, but they may be opinions not supported by best scientific evidence. 

I think the limbic system, in particular amygdala and hippocampus would be activated in both, and in many other emotional reactions.

But even more relevant, given that this is cog-sci exchange, is that there is the idea that fear and anger are cognitively similar in that they both focus and narrow the mind, but that anger focuses the mind much more because fearing a certain object also makes one hypervigilant so the person could potentially react to lots of other potential signs of danger at the same time.  But my thinking is that anger can also lead to arousal and person being irritated by lots of other previously-neutral stimuli.

Another idea I remember is that apparently fear leads to feeling cold in the extremities but anger the head and particularly the arms can remain or get warmer.  Or as this NPR article says, fear leads to feelings in the chest area, but anger is one of the few feelings that activates the arms.

Internally it is my own experience that fear leads to shrinking and weakness while anger leads to a kind of activation and strength.

Externally there are behavioral differences but also in terms of body language and facial expression, apparently one can tell anger and fear apart.  Clenching jaws and fists in anger...

But the problem is people rarely express these emotions so fully in their body or their face.

Or to be more accurate, it depends on the person and how expressive they are and how frightened/angry they feel, culture, age, etc.  But such facial expressions as ones below are not ones I see around me often.

http://www.cs.unc.edu/~andrei/expressions/

Lastly, I once had a talk with a doctoral candidate and very briefly we touched on this, which is obviously quite a big topic, but he told me one of the difficulties is that the feelings that follow each other very fast and also that a person might react to feelings with other feelings.  For instance, you become angry at your child but then almost instantly you might feel fear at how angry you are, etc.

So the above are sort of what I've read or remember about the differences.  I really like to learn more about this so if you feel this question is too broad, just choose the area that you know most about and correct my thinking there.  Since this was the only psychology section of the forum, I posted it here, and surely anger/fear distinction not only can be studied by different branches of psychology (biopsych, behavioral psych, cog psych, clinical psych, etc), but as a human emotion, it can also be studied by anthropology, for instance, on the cultural level.  So I'm aware of that.
The most conservative answer is that we can reliably distinguish anger from fear if we constrain our examination to a particular context, a set of stimuli, or a person.   However, studies on emotions within single individuals have only begun to attract funding, so we don't quite know yet how well we can do this.

If we ignore contextual and individual differences, then our ability to reliably distinguish between these emotions drops significantly. This is because fear and anger can manifest very differently depending on the context and/or person (there's large variability in a bunch of response systems: facial, bodily, neural, behavioral, etc.), which prevents us from classifying them accurately or in a perceiver-independent (i.e., objective) way.

But let's look at some papers...

Brain

Here are the results from this meta-analysis for anger and fear:




Body

I've read a meta-analysis under review that used fancy statistical analyses to distinguish emotions by physiology.  The conclusion was that we can't distinguish emotions based on physiological variables, so as of right now we don't believe there are reliable physiological differences.

For relevant reading, see this paper, which provides a systematic qualitative review.

Face

This is still under study.  The idea of universal facial expressions is incredibly controversial (e.g., Nelson &amp; Russell, 2013), so it's best not to take it as fact, independent of your theoretical orientation.  It's quite possible that under many circumstances we can distinguish "anger faces" and "fear faces," but others we cannot. 

However, the most important point is that it's not even clear that we can reliably know that an "anger face" is actually an "anger face" and a "fear face" is actually a "fear face," given that there can be so much variability in facial production and perception (e.g., this recent study).  I've never even seen Ekman's "universal" fear face in real life.  

Behavior

Anger and fear are traditionally contrasted in terms of approach and withdrawal, respectively.  However, this probably isn't a reliable difference (e.g., this paper), as it depends on goals, environmental constraints, etc. 

Overall... it's pretty difficult to objectively determine if someone is experiencing a certain emotion, let alone distinguishing between two of them. We might be able to do it better as we take a more idiographic approach, but studies like that have only begun to emerge.  Some people argue that multivariate analyses are the answer, but even these aren't reliable classifiers from one context to another.