'Site' is (architecture) to situate or place a building while spot is to see , find; to pick out, notice, locate, distinguish or identify.

A spot and a site can be the same as Rich said. However, generally a spot is a very small area whereas a site is a larger area. We may sit in a shady spot under a tree when we visit a tourist site, historic site or a building site.

"Spot" feels a lot more casual. Here in the United States we use it to casually for places, especially with positive adjectives: - I found a nice spot for lunch - This is a good spot to sit down "Site" is often used in common phrases, like: - Camp site - Tourist site - Construction site But "site" isn't used very casually like "spot".