{bam} is defined as "face, have the prospect of having to deal with".

{DIgh}, on the other hand, is defined as "undertake, deal with".

I can't understand what's the actual difference between them. 

Do we use {bam} when we will face something unpleasant in the future, and {DIgh} when we deal with something in the here-and-now, regardless if it is pleasant or not ?

That's pretty much it. bam doesn't imply unpleasantness, though it'll often be used of something unpleasant (otherwise why mention facing it?). You might say noH wIbam. ngay' vIchav! We face a war. I will achieve glory!

-- 
SuStel
http://trimboli.name