¿Cuál es la diferencia entre notice y realize ?Puedes dar oraciones como ejemplo.

They are very similar and can usually be used interchangeably, but usually have slight nuances in different situations.

For example:
"I noticed there was a pencil on the floor." - feels like a casual, unimportant discovery that you quickly find out

"I realized there was a pencil on the floor." - puts more emphasis on finding the pencil on the floor / more of a discovery of knowledge that has more thought

Another example where they have quite different nuances:
"I realized that he loves cake." - Discovered and strongly knew that he loves cake

"I noticed that he loves cake." - discovered that he loves cake, but no real emphasis of the knowledge