Are there reliable ways to distinguish anger from fear, be it through body, mind, internally, externally?
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.