Post and Lintel construction involved simply using two or more "posts" which would be vertically standing supports to hold the "lintel"; this was seen a lot in Greek construction with their columns and large open spaces between. This method would've been restricted mainly to gates or openings with 90 degree angles. Vault construction techniques involve interlocking bricks or stones and using counter resistance which allows you to create curves and arches... these were used a lot in cathedrals and churches to make the curved ceilings.
