In some sense, the answer to these sorts of questions is always something along the lines of “there are no rules”. You can build you model in any way you see as appropriate. That being said, there are likely to be conventions that exist within the area you happen to working in. Some common likelihoods can be see in this list provided by Bambi. The Weibull distribution is commonly used to model the survival function in survival analyses (e.g., here). But there are probably lots of other applications that I don’t know about.