The Oxford English Dictionary defines each as:
Mobile Phone - A portable telephone.
Feature phone – Any of various telephones enhanced with computer technology; (later chiefly) spec. a mobile phone incorporating features such as Internet access and music playback, but lacking advanced functionality such as the ability to run general-purpose computer applications;
Smartphone - Any of various telephones enhanced with computer technology. Later chiefly: spec. a mobile phone capable of running general-purpose computer applications, now typically with a touch-screen interface and Internet access.
If you read the above, it will be clear to see how there is not a great deal of difference in the definition between a feature and smartphone.
This is what has been occurring in the mobile space for some time. Many of us now own a smartphone often because the prices of smartphones not to mention the capabilities make it the better option to go for.
I encounter people looking for a basic mobile, through to a smartphone, but modern terminology has confused those who are less interested or technically aware. It is not uncommon to find someone who needs a basic mobile phone and what in my mind is not even a feature phone. On the other hand I get people who say they want a smartphone when really a feature phone would suit them better.
But what do we refer to is as? Is it our mobile phone or our smartphone?
Few would refer to a a feature phone, but many still own a feature phone.
I have come across a bit of snobbery in my time, those who do not have a mobile phone they have a smartphone.
Ultimately the term is interchangeable as a smartphone is still a portable telephone and the vast majority of new mobile phones are smartphones. I refer to each model as a smartphone but when asking someone what device they use, I would ask what phone do they have.
What name do you tend to use or is it a combination?