What's the difference between "Fireplace" and "chimney" in english?

Fire place is the opening where the fire is, the hearth. The chimney is the structure that carries the smoke out through the roof, the stack, usually brick / stone built.

The fireplace is where the fire is and the chimney is where the smoke from the fire goes.

A chimney leads from the fireplace up through the house to the outside.

A fireplace is the space where the fire is located. A chimney is the structure through which smoke passes to the outside.

A fireplace is exactly what it says, the place where the fire is. The chimney is the pipe leading from the fireplace to the roof to take away the smoke. 

They are 2 different things.

The fireplace is in the room.

You put wood into the fireplace.

The chimney is above the fireplace.
The chimney may be hidden in the wall, or visible, but it carries the smoke up from the fireplace and out of the house.
You can see the chimney on the outside of the house.

A fireplace is the protected area INSIDE a dwelling in which a fire is laid and burns. a chimney is the vent for the fireplace, the vertical, mostly-exterior structure that serves as a channel for the smoke created in the fireplace.

A fireplace : an open recess in a wall of a room, at the base of a chimney
A Chimney:  A passage through which smoke and gases escape from a fire or furnace; a flue.

Hello there,

I will do one better than that,  go and have a look at this page on fireplace history as it will tell you why there was a chimney in the first place.

You might even have a little bit of a laugh... Happy reading

Put the coal in the fireplace, build the fire and light it,  and the chimney conveys the smoke  outside.

For additional points you can also use "hearth" for "fireplace" and "flue" or "stack"  for "chimney"