I'll start with the commonly known stuff, that are currently talked about the most.
All x86 processors are developed from the CISC (Complex Instruction Set Computers) architecture. The x86 processors allow you to perform several activities at the same time from a single instruction. Also, they can perform numerous simultaneous tasks without any of them being affected.
This makes them very sophisticated and advanced processors, allowing many complex calculations in a short time. The disadvantage of this design is that they need a lot of power to function and more power means more heat.
Summary: x86 chips are designed to be power hungry and high clocked, multi-thread, high instructions per cycle. In the general use-case they will be a lot faster than your common ARM chip.
As for ARM processors, they are based on the RISC (Reduced Instruction Set Computer) architecture, which is much simpler than CISC. These processors can do a much smaller number of calculations since they require several commands to act.
RISC instructions are smaller and faster to process, so in part, the disadvantage of having to process several commands for a single action is minimized. Still, ARM processors are much less powerful than the x86.
Summary: ARM chips are designed for low power draw, flexibility, low cost and low heat with good performance.
source of the info above
M1 is not a CPU. It is a whole system of multiple chips put into one large silicon package. The CPU is just one of these chips. And that's the main reason why it's so different and fast compared to the typical ARM chip.
Basically, the M1 is one whole computer onto a chip. The M1 contains a CPU, graphical processing unit (GPU), memory, input and output controllers, and many more things making up a whole computer. This is what is call a system on a chip (SoC).
In the past computers would have multiple physically separate chips on the motherboard of the computer. However because we are able to put so many transistors on a silicon die today, companies such as Intel and AMD began putting multiple microprocessors onto one chip (CPU cores). One core is basically a full independent chip that can read instructions from memory and perform calculations. This has for a long time been the name of the game in terms of increasing performance - just add more general-purpose CPU cores.
Instead of adding ever more general-purpose CPU cores, Apple has followed another strategy - they have started adding ever more specialized chips doing a few specialized tasks. The benefit of this is that specialized chips tend to be able to perform their tasks significantly faster using much less electric current than a general-purpose CPU core.
Hope that answers your question.
You can find more details on the M1 where I got the info for the second part of the answer. There is a lot of additional and interesting info on the CPU market and the software differences inside the M1 and Intel/AMD chips: link