MOTHERBOARDS (God help us all).
Motherboards link all the components together and help them talk to each other.
A few key things:
Motherboards come in different sizes. ATX is the standard size, but you may see MicroATX, ITX, etc. ATX boards will have several expansion slots. MicroATX will only have one big slot for graphics cards. For a budget build I'm not sure you'd need more than one big expansion slot but MicroATX boards aren't necessarily less expensive.
M.2 slots are slots for a certain type of storage drive. Like other things, there are generations but they are compatibile. If you get a good deal on a 4th gen M.2 SSD you can plug it into a motherboard with a 3rd gen slot but you'll get 3rd gen peformance. Not every motherboard will have an M.2 slot. If your motherboard doesn't have an m.2 slot then don't buy an m.2 drive.
A "chipset" is the controller on the motherboard that communicates with the CPU and other components. The CPU has to be compatible with the chipset in order to function. This is something covered for you with the compatibility checkers.
RAM Type - DDR4 is the "older" standard but is still great for gaming and will be for a long time. When you look at motherboards consider RAM compatibility and cost. You should be looking at DDR4 IMO. Way less expensive.
INTEL
Each generation of Intel CPUs have their own socket designs. The socket is what the CPU slides into and sits in on the motherboard. Compatibility checkers will help get the right socket. This is designated by "LGA ####."
You'll notice each Intel motherboard starts with a letter.
The "Z" series is the higher end, capable of overclocking, and has the most ability to run a bunch of fast hardware all at once. Generally these aren't great value for budget builds unless they come in a bundle for a big discount.
The "B" series is midrange for Intel. They don't overclock. They have ample lanes to run hardware fast and are usually the better value proposition
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The "H" series is the budget line. It limits RAM and USB speed as well as has the fewest "lanes" for traffic along the board. Generally these get put in ultra-budget builds.
The number after the letter is the generation of chipset and don't worry about it unless you don't use a compatibility checker.
AMD
Similarly, there are different motherboards for different CPUs. Their sockets are designated by "AM-". AM5 is the current gen socket for "7---" series and up. AM5 requires DDR5 RAM which is more expensive.
Similar to Intel, the letters designate capability.
"X" is their higher end, "B" is their midrange, and "A" is their lower end. The number after designates chipset and don't worry about it as long as you are using compatibility checker.
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Each motherboard manufacturer puts their own branding all over everything but what you want to look for are the m.2 compatibility (unless you want to go SATA which may be cheaper), RAM speed compatibility, and overall quality. I can tell you ASUS has been under a lot of criticism for their motherboard quality over the last few years along with their return/repair customer service so may want to steer clear.
