There is ground tea and then there is milled tea. There is a difference. Actually, there are various grades (particle sizes) of tea powder. I bought a cheap one called "fen cha" 粉茶 which means "powdered tea" - but it's coarse as hell. I could make a finer grade of tea powder using a small stone mortar. Then there is machine ground tea powder - which might look fine, but is actually too coarse and unsuitable as matcha. You could make such a tea powder using a blender or coffee mill at home.

But to really get tea powder down to the fine grade for matcha, you need a heavy stone mill. I say heavy because even a portable, light mill won't produce a satisfactory result.