There is no difference between the smartphone and the iPhone. iPhone is a smartphone and smartphone is an iPhone.
The word smartphone indicates all phones which are very smart devices (for making calls, texting, sending emails using navigation etc…).
So basically the smartphone is a word like cars.
You have different manufactures of cars: Honda, BMW etc….
And you have different manufactures for mobile phones: iPhone, Samsung, Huawei etc…
Example: smartphones of diffrent manufactures: