...Well, you got the basics.
A Dalek is an alien from a planet called Skaro. The inhabitants of that planet are called Kaled. Which are actually supposed to be peaceful if I remember correctly, but some of the Kaled are taken and have all emotions wiped from their minds except hate. They are then put into the metal "robotic" shell and called Daleks. (Also Dalek is an acronym for Kaled, which explains why they are called Daleks.)
The TARDIS is a time machine that is bigger on the inside. It is not really a "Phonebooth" it is only disguised as one. The TARDIS has the ability to disguise itself as an object nearby where it lands so it doesn't draw suspicion by looking out of place, but The Doctor's TARDIS has a problem with it's disguise mechanism so it is stuck with the appearance of a phonebooth permanently.