Well, poslat has a range of variety where it could be used. For example you could say 'Poslal som list' - I sended you the letter. Or you could use it when you send someone somewhere(e.g to do something). 'Poslal som ho do obchodu' I told him to go to the shops. The word ,,zaslať " is from the word 'zásielka' (package) and therefore would be used in the context when you send something (e.g mail, letter..) So for example you could say 'Zaslal som list' (I sended you the letter). However saying 'Zaslal som ho do obchodu' would not make much sense.

I dont see much difference between those two words, but the word ,,poslať " is more commonly used.