What is the real meaning of an integrated graphics processor?

I was looking up the specifications of a central processing unit i needed to buy for an upgrade and then I noticed that in the product description of the processor, they had indicated intel hd graphics 500,which raises the question, how can an onboard iGPU be switchable unless the graphics processor is inbuilt into the cpu itself.

You cannot; An Intel iGPU will always be part of the processor so it’s impossible to change your Intel GPU without changing the processor in your system.

So my questions are: Does changing a processor change the iGPU if its cpu inbuilt and then how do you know if your onboard graphics processor is on the motherboard or inside the cpu?

The only way to upgrade an Intel iGPU is to upgrade the processor.

I also noticed several websites associating certain processors with the onboard gaphics processor, for example an i7-3770 uses an intel hd graphics 4000 and an i5-3570 uses an intel hd graphics 2500.

As for Intel HD Graphics 2500 and Intel HD Graphics 4000 they are the same generation but different generation tiers. Both of those Intel iGPUs were from the third generation but had a slightly different amount of shaders. This is essential what Nvidia has done with their GeForce 30 series cards by releasing the GeForce RTX 3080 in 2020 and the GeForce RTX 3080 Ti in 2021