Motherboard form factor decides how large a case you need, how many expansion slots and memory slots you get, and how difficult the build will be. The differences are more consequential than the size numbers suggest.
ATX
305 × 244 mm, the full size. Usually four memory slots, several expansion slots, the most USB and storage connectivity, and the most room to work in.
The default choice unless you have a reason to go smaller. Cases are roomy, cable routing is easy, and cooling is straightforward.
Micro-ATX
244 × 244 mm. Usually four memory slots, one or two fewer expansion slots.
For a build with a graphics card and nothing else in the expansion slots, which describes most builds, you give up very little. Boards are often cheaper than the ATX equivalent, and the cases are smaller without being cramped. It is the most underrated of the three.
Mini-ITX
170 × 170 mm. Two memory slots, one expansion slot, fewer M.2 slots and fewer ports.
Real constraints follow. Two memory slots means a four-module kit will not fit and upgrading means replacing what is there. One expansion slot means the graphics card and nothing else. Cooler height is limited, cable routing is genuinely difficult, and components run warmer in a smaller volume.
Mini-ITX boards also cost more than larger ones with the same chipset. Choose it because you want a small machine and are willing to work for it, not to save money.
E-ATX, and why it needs care
E-ATX is not one standard. The name covers a range of widths, and manufacturers apply it inconsistently.
A case advertising ATX support will not necessarily take an E-ATX board, and where it physically fits, the extra width often covers the cable routing openings along the edge of the tray, which makes the build considerably more awkward.
Only buy an E-ATX board into a case that explicitly names E-ATX support. Our PC Builder treats this strictly for exactly this reason.
What you actually lose going smaller
Expansion slots are the headline difference and the least relevant one for most people. A build with a graphics card and nothing else uses one slot, and the rest go unused regardless of board size.
The differences that matter more in practice are memory slots, where Mini-ITX gives two rather than four and removes the option of adding capacity later, and M.2 slots, where smaller boards have fewer and you may run out sooner than expected.
Connectivity also thins out. Fewer USB ports on the rear, fewer fan headers, fewer case connectors. A Mini-ITX build with several case fans often needs a separate fan hub, because the board has two headers.
Cooler clearance is the constraint people hit hardest, and it is a property of the case rather than the board, but the two go together: small boards go in small cases.
Micro-ATX is the one to consider more often
The usual decision is framed as ATX or Mini-ITX, and Micro-ATX gets skipped. That is a mistake for a lot of builds.
It keeps four memory slots, takes a full-size graphics card and a full-size air cooler, uses standard ATX power supplies, and fits cases that are noticeably smaller than a full mid tower without being difficult to work in.
What you give up is two expansion slots most builds never use. Boards are frequently cheaper than the ATX equivalent with the same chipset, because they are positioned as the budget option rather than being less capable.
If you want a smaller machine but do not specifically want a small one, this is usually the right answer.
A smaller board generally fits a larger case, because the mounting standards share hole positions. Confirm the case lists the size rather than assuming, since some compact cases only provide standoffs for the sizes they name.