mugging = being attacked and robbed in the street or another public place

Using the dictionary definitions of the words, "being mugged" and "being robbed" have the same meaning. However, "being mugged" suggests a violent, in-person confrontation (meaning someone drew a knife or pointed a gun at you). "Being robbed" technically means the same thing but the meaning has broadened over the last couple centuries to mean "I was stolen from". A "bank robber" is one who goes into a bank and holds a gun at the bank teller and demands money. However, one might also say "the bank was robbed of $10 million by hackers with a Russian IP address". Another example: if you go to buy a car and wind up paying more than you should have, you might say "I was robbed!". The car dealer didn't actually steal from you but he may have cheated you by getting you to pay more than the car was worth. Or, in a different situation, you could say "I was the best candidate for that job but I was robbed of the opportunity that I deserved because the boss hired his friend's son instead." It's less common to use "mugged" in these kinds of metaphorical expressions.