Should baseboards and window/door casings be the same size?

That totally depends on you taste and no one else

It should be okay to do the same size or the baseboards a little larger. I have seen it done both ways and they look fine.

Not necessarily, our door casings are a smaller than the baseboard and they look great!

Window and door casing should match in the same room. Not necessarily throughout the house. Baseboard generally is not the same size as door/window molding, but a similar style. Most of the baseboard molding is larger than door/ window casing.

It's all about scale. They should be in the same scale. Check your local home improvement stores. You will see various trims stocked together. There are small scale trims, large scale trims and the average sizes. Choose all your trims from the same grouping

Depends partly on the style of the house and how important wood, or trim, is to the design. My house built in 1904. My door casings are a bit narrower than the baseboards but have crown molding ar the top. The windows ever so slightly narrower, but again crown at the top. Moderne houses have minimal “trim”.Whats your style goal? Look at a lot of Houzz and Architectural Digest and decide