Standard piano music consists of notes in the bass clef for the left hand to play and notes in the treble clef for the right hand to play. Regular piano lessons teach you to read both clefs and over time and practice, one can become proficient at reading music for both hands. Below is an example of standard piano music.
Chord piano, on the other hand, has only a single note in the treble clef for the melody and chord symbols above the notes to indicate the chords played with the melody. The melody is always only one note, and usually played by the right hand, so you don't have to be able to read several notes to play at one time. Over time and practice, your left hand will "memorize" the chord and you will be able to play it effortlessly when you read the symbol. Also, once both hands learn chords, you can then start learning different chord patterns to play to "dress up" the music and embellish your songs.
Here is an example of a lead sheet (chord piano music):
