See the diagram below.
is the height, and 
is the slant height.
The height is the distance from the base of the pyramid to the vertex (the top of the pyramid). It runs perpendicular to the base.
The slant height is the distance from the base of the triangles which make up its sides to the vertex. It runs perpendicular to this base as well.
The height is the distance from the base of the pyramid to the vertex (the top of the pyramid). It runs perpendicular to the base.
The slant height is the distance from the base of the triangles which make up its sides to the vertex. It runs perpendicular to this base as well.