The atmosphere consists of many layers. From the ground up, these are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere.

You may be thinking of the thermosphere, which is indeed very hot (thus the name), albeit with such low density that it wouldn't transfer much heat to your spacesuit or spacecraft. But the thermosphere is part of the atmosphere too.

https://spaceplace.nasa.gov/thermosphere/en/

The ISS and other low earth orbit satellites are orbiting inside the thermosphere. Yes, the ISS is in the atmosphere and suffers from a small amount of atmospheric drag, so it requires occasional reboosts to maintain altitude.

The ionosphere isn't exactly a separate "layer" from these. It's a very tall region of ionized gas that starts near the top of the stratosphere and overlaps parts of the layers above. Its exact limits vary with solar conditions.

The ionosphere is actually made up of several layers of its own, defined by the solar energy wavelength that causes ionization in each layer. These are the D, E, and F layers, and occasional sub-layers within those. Hams and other shortwave radio operators are familiar with these ionospheric layers because of their different effects on radio propagation.

https://en.wikipedia.org/wiki/Ionosphere

https://spaceplace.nasa.gov/ionosphere/en/

https://www.nasa.gov/mission_pages/sunearth/science/atmosphe...

And I finally get to say about one of my own comments: "Username checks out."

https://en.wikipedia.org/wiki/Stratoscope

(I'm actually named after the Truetone Stratoscope radio antennas, not the balloon, but sometimes people do say I'm full of hot air.)