Our Gemara quotes Rava (some say it was Rav Pappa) as ruling that in cases where two people interact and both end up injured, the liability of each one will depend on what happens. If both parties had permission to be there or if neither one had permission to be there then, “Hiziku zeh et zeh hayyavin, huzku zeh ba-zeh peturim – if they did damage to each other they are both held liable; if they were damaged by one another then neither one is held liable.”
The difference between the two cases as presented by the Gemara is not entirely clear. This is particularly true according to Rashi who suggests that the case of hiziku is one where people tripped on each other, and would be responsible for damages done to the other since a person is considered mu’ad le-olam – always responsible for his actions and their ramifications. Thus it is not clear what would be a case of huzku as opposed to hiziku.
The Ra’avad explains that the cases cannot be talking about situations where the two people tripped on each other simultaneously, rather where one person injured the other directly (hizik) or indirectly (huzak). For example, if a person was lying on the ground and a second person stepped on him and injured him, the person who directly caused the injury would be held liable. If the second person had tripped over him and become injured, the person lying on the floor would not be held liable, since his involvement in the injury was indirect. The Rambam appears to distinguish differently, explaining that hizik means a person who intended to perform the act that injured his friend while huzak refers to a situation where the act was done without intent.
The Gemara concludes that these rules only apply because both parties had the right to be where they were. If one of them had the right to be there and the other did not, the one who was not allowed to be there would always be responsible for the damage that was done.