ARM is a Micro - Controller designer (In General) and makes few micro - processors to for low end laptops with not a very high capability as that of Intel, whereas speaking of x86, it requires several other components such as RAM, Motherboard, etc. to function upon.
ARM inputs within itself the data signals which are derived from the battery of the Mobile Device and functions.
x86 on the other hand needs comparatively heavy power supply to power up the motherboard.
Besides when talking about x86, we mean only a Micro - Processor and not a Micro - Controller.
The difference lies within their functioning.
A Micro - Processor is only an accumulator and generator, i.e., it accumulates signals in binary and processes them. The motherboard it is embedded in channels the signals to various devices and they work accordingly. A ram is also necessary for quick functioning of the Micro - Processor commands or even beneficial to store in the data for a temporary period of time which can be POPPED or PUSHED by the Microprocessor.
Speaking of a Micro - Controller, it generally has an inbuilt RAM, 16 - 32 pins (even 48 or more). These pins do some or the other functioning of your mobile device. A Micro - Controller Pin can be programmed using C or Assembly to light up the screen, Turn on the Led, etc.
Now the main point of difference is that the power consumption of the x86 is high. But in recent days the Intel Technology have started making tablets which power a partial part of x86 and process just as a computer would do making data management, gaming, etc. amazingly fast.
Hope that helps Sir :)