The azimuth and elevation spherical coordinates are a mean to define a direction in a three-dimensional space. How you define which angle is the azimuth and which angle is the elevation is up to you. It's like setting up a (x,y,z) coordinates referential
Azimuth/Elevation diagrams shows the antenna's gain along those directions. Sometimes, we talk in E-plane and H-plane but those are different definitions, which are totally dependent on how the antenna is polarized.
They can be related to azimuth/elevation, but the convention that links the two is author-dependent.
Example : A dipole antenna E-plane would be the one including the antenna itself while the H-plane would be the one perpendicular to it, like in :
In your example datasheet, we have the following information about the E-field :
Polarization : vertical
Which indicates than the E-field lines are contained in vertical planes (containing the antennas vertical axis). Therefore, you can safely assume that the E-plane was chosen arbitrarily among the infinity of possible choices (every plane coplanar to a E-field line is a E-plane) and the H-plane was defined as its perpendicular plane. Both elevation and azimuth are defined in an implicit maner, but common sense would recommend elevation for E-plane and azimuth for H-plane, in this particular example.