So, for Brazil (not sure if it would be any different in other places):
Primarily: Mala = suitcase
Then, secondly, mala = trunk if you're talking about a) the back of the car where you put the stuff, or b) the... human body xD
A travelling trunk (like the one they used in Harry Potter) would rarely be considered a mala. It might be called a mala baú (if you're looking to buy it online, for instance), but really we just called it a baú
Last but not least, a duffel bag and any of those bags that you use for travelling but are not really suitcases, are also called mala - so this is one instance I can think of where mala could be translated as bag, but it just won't work for any bag (you can't call a grocery bag a "mala")
As for the case/briefcase, we usually call them pasta or maleta - but you could have a mala de dinheiro (case full of money), I've seen it used like that in movies, at least - I've never seen an actual case full of money in real life, so...
Hope this helps. If you still have questions, just ask C: