Dots modify notes by extending their durations. When dotted, a note (or rest) is held for
Here is an example using mixed durations along with dotted notes and a rest.
Ties connect two or more notes of the same pitch so as to extend the initial note for the desired duration.
A primary use for them results from the fact that individual note durations are not allowed to span bar lines. Ties are therefore employed to hold notes over from one measure to the next.
Though less rigorously adhered to, traditionally there is also a proscription against spanning what is referred to as the imaginary bar line, an invisible line that divides every measure in half. In this case, ties are used to best maintain readability.