External Pressure: ASME VIII-2 2007 Par 4.4

Take your sphere and inject high pressure gas into it - internal pressure.

Now take your sphere and place it under water - external pressure.

It is more common in multichambered vessels, for example a tower with an internal head separating the top and bottom chambers - perhaps the higher pressure chamber is the top one so you would have place the head with the concave side to it - when the lower chamber is pressurized, it would push on the outside (convex) side of the head, external pressure.

Also this phenomena may be found in shell and tube heat exchangers. Pressurize the internals of the tubes and you have internal pressure. Pressurize the shell side of the exchanger and you put external pressure on the tubes.