When you say "spread the chord" and "spread the notes," it sounds like you might be talking about "arpeggios" or "broken chords." "Arpeggio" comes from "harp," and apparently refers to the way the notes of a chord are played at different times rather than all at once when the strings on a harp are strummed or plucked.
The most basic type of arpeggio is where you "roll" your hand when playing the chord, so that the notes are quickly played one after the other, similar to the way a chord sounds when a guitarist strums across the strings. This is usually done left-to-right, such that the lower notes are played before the higher notes, and is written as a chord with a squiggly vertical line immediately to the left of the chord. But it can also be done right-to-left, such that the higher notes are played before the lower notes, in which case a downward-pointing arrow is drawn in front of the squiggly line. In both cases you hold the keys down after you play them-- i.e., you do play the notes together as a chord, you just don't strike the notes at the same time.
More advanced or complex arpeggios can also be played, which usually involves playing the notes in some repetitive sequence, such as up-down-up-down (e.g., C-E-G-E, C-E-G-E, etc.). In this case the notes are played separately rather than being held down after they're played, so you aren't playing them as a chord per se, although they're usually notes that would form a chord if they were played together.
Arpeggios are an extremely common technique when playing synthesizers, although they aren't usually played "manually"-- rather, a built-in pattern sequencer is programmed such that all you need to do is hold down a note, or two notes, or a chord, and the synthesizer will play a pattern (i.e., arpeggio) based on the notes you're holding down. Portable electronic keyboards (Yamahas, Casios, etc.) will often include an arpeggio function that can be used with a variety of pre-programmed arpeggio patterns.