Hi there,a nice question that is asked by a lot of non-native learners!They have a slight distinctive meaning.
Erkek is a male gender name for all kinds of beings(including humans).For woman it is (dişi)
Adam is the Turkish counterpart of the word ''guy'',and adam also can be used as an indefinite pronoun for males but it is not an indefinite pronoun.(adam gel-di/o geldi/he came...) For your question,we have to inspect the sentences pragmatically:even though adam is an acceptable and a correct translation,I think the more accurate one would be to use the word erkek since the sentence is about the general terms and not about the gender specifics.All in all,you have a good understanding of their distinction.Hope this help!Cheers!
Rica ederim!Tabii ki!That's right,you can say that erkek is the counterpart of dişi,well done!And for your information,here are some examples:
Bu kuşların cinsiyeti ne?(What is the gender of these birds?
Erkek kuş,dişi kuşu sever. (Male bird loves the female one/bird.)
Adam ağladı.(The man cried)
Kadın ağladı.(The woman cried)