Solow Model: Steady State v Balanced Growth Path
This is when the attempt at accuracy creates confusion and misunderstanding.  

Back in the day, growth models were not incorporating technological progress, and led to a long-run equilibrium characterized by constant per capita magnitudes. Verbally, the term "steady-state" seemed appropriate to describe such a situation. 

Then Romer and endogenous growth models came along, which also pushed the older models to start including as a routine feature exogenous growth factors (apart from population). And "suddenly", per capita terms were not constant in the long-run equilibrium, but growing at a constant rate. Initially the literature described such a situation as "steady state in growth rates".  

Then it appears the profession thought something like "it is inaccurate to use the word "steady" here because per capita magnitudes are growing. What happens is that all magnitudes grow at a balanced rate (i.e at the same rate, and so their ratios remain constant). And since they grow, they follow a path..." Eureka!: the term "balanced growth path" was born.  

...To the frustration of students (at least), which have now to remember that for example, the "saddle path" is indeed a path in the Phase diagram, but the "balanced growth path" is only a point! (because in order to actually draw a Phase diagram and obtain a good old long-run equilibrium, we express magnitudes per effective worker, and these magnitudes do have a traditional steady-state. But we continue to call it "balanced growth path", because per capita magnitudes, which is what we are interested in, in our individualistic approach), continue to grow).

So "balanced growth path" = "steady state of magnitudes per efficiency unit of labor", and I guess you can figure out the rest for your phase diagram.