Are the iPhone XR and iPhone 12 the same size?

No. See the comparison below.

https://www.apple.com/iphone/compare/?modelList=iphone12pro,iphone12,iphoneXR

They have the same screen size, which is 6.1” measured corner to corner, but the IPhone 12 is slightly smaller and a bit lighter too.

IPhone XR

150.9 x 75.7 x 8.3mm,

194g

iPhone 12

146.7 x 71.5 x 7.4mm

164g