Laptops:
Pretty much all Intel laptops with a discrete GPU take advantage of software to decided which GPU to use for specific applications. Nvidia's Optimus is a good example. AMD has something similar though I can't recall off the top of my head what it is called.
AMD pretty much sells laptops with APUs or Intel/AMD systems. Just recently the first Ryzen/AMD graphics laptops are starting to appear. Since Ryzen doesn't have integrated graphics not really on topic.
Recent Desktops:
Intel HD Graphics are included on the CPU die, when a discrete card is plugged in it typically becomes disabled. On some motherboards, running a display from the iGPU is supported even when a discrete GPU is installed. Applications will only be able to make use of one or the other though.
AMD's APUs use the same graphics cores as many desktop graphics cards. They supported a mode called Dual Graphics, which let the GPU resources on the APU be used in conjunction with a graphics card. It was limited to a fairly narrow scope of GPUs, and wasn't that useful, but it was a way to use both.
Older Desktops:
Graphics used to be integrated into the motherboard, pretty much the same way laptops of the time did before fully integrated GPUs. So you could commonly find motherboards with Nvidia or Intel graphic chipsets on board. These still used system memory, albeit a little slower.
If anything, when completely off, the onboard GPU of Intel chips acts as part of the heatsink. These days the majority of the silicon is used in the GPU section.