Is a .243 caliber bigger than a 22-250 caliber?

Yes, the bullet is bigger in both diameter (.243 versus .223) and weight. The .243 can use bullets that weigh up to maybe 130 grains, which is a lot more than most .22-250 bullets weigh.

But the .22-250 fires at a faster velocity, so it is sometimes the better choice for varmint hunting.