“primary school” means“小学”，“小学校”不对，中国人很少用。

小学 is refers to Primary school 小学校 is refers to the size of the school is very small

if you want to express "primary school",we use 小学。no 小学校。 or you can say :小学学校 to express "primary school"

When Taiwan in Japanese-Occupied Period, "小學校" means "primary school". But now we only say "小學"; nobody say "小學校" Japanese-Occupied Period is the Japanese colonial period in Taiwan. It refers to the period between 1895 and 1945 during which Taiwan was a Japanese colony.

Honestly I have never heard someone saying 小学校, so I consider they are different. My explanation is as follow. 小学 is a term for primary school. 小学校 sounds not so good. You can say 小的学校, in this case, it means a small school, no matter this is a primary shcool or middle school. So the amount of students and the area can be both small.