Peter wrote:
"----- it is a challenge to make it clear and consistent."

For me. no one does a better job than Dr. Frederick Emmons Terman who
wrote on page 1 of "Electronics and Radio Engineering":
"Electrical energy that has escaped into free space is in the form of
electromagnetic waves. These waves, which are commonly called radio
waves, travel with the velocity of light and donsist of magnetic and
electric hields that are at right angles to each other and also at right
angles to the direction of travel."

The rest is in the book which should be consulted for a complete
definition.

Best regards, Richard Harrison, KB5WZ5