1) The scientific meaning of 'climate' is the average of the weather in a place over a long period of time. For instance: "The climate in London is cool and wet".
2) 'Climate' can also mean the feeling you get in a room perhaps caused by a group of people who are angry about something. In that situation you would might say: "the climate in here is hostile".
3) In scientific terms 'atmosphere' is the air that we breathe; the collection of gasses that exist from the ground upwards and which gradually reduce as we climb higher -- until none are left by the time we reach space.
4) 'Atmosphere' can also mean the same as 'climate' (as in 2). So when you enter a room where people are angry you might say: "there's a very aggressive atmosphere in here."
So in non-scientific use 'climate' and 'atmosphere' are interchangeable.