I'll try to give a simple answer.
Smartphone - phone which you an install apps on and has good internet integration
i-pod - generic name for a music player. iPod is an is an Apple brand of music player
Androids - a phone or tablet running the android operating system and can use android apps.
There is some crossover with bigger phones that almost approach the size of tablets. A smartphone can do everything that a ipod can do as well as make phone calls. A tablet is like a big ipod so you have a screen that is easier to watch movies on and read books on.