I see no difference between the two as far as the meanings from various dictionaries are concerned.
From Cambridge dictionary:
the clear, salty liquid that you pass through your skin:
The dancers were dripping with/pouring with sweat after a morning's rehearsal.
By the time we'd climbed to the top of the hill, we were covered in sweat.
She wiped the beads (= drops) of sweat from her forehead.
polite word for sweat (= to pass liquid through the skin):
He was perspiring in his thick woollen suit.
The journalists and camera crews began to perspire in the heat as they stood waiting for the president to appear.
But recently I heard from someone that only animals sweat but humans don't, humans perspire. So I googled for it found this. I quote an interesting answer from the link
He must be quite an old-fashioned English person. I remember this view being expressed by my grandmother, who was born in about 1885. I haven't heard it recently.
Is it justified to say animals sweat, humans perspire? The only difference that I see between the two words is that the latter is more formal version of the former. Is the last quote that says such difference existed in the olden days correct?