I'm getting confused as to the difference between a riff and a chord progression.

Some one told me that smoke on the water is not a chord progression but a "riff" a melodic figure. I have a book with the song transcribed and above that main riff it just says "Gm" as the chord. I know that power chords are not technically chords but you could play the main "riff" to smoke on the water as full chords. Does that make it a "progression" or is it still a melody?

Then there's the riff to seek and destroy by metallica. I was told that there is no progression it is just "riffs". Melodic figures. I thought everything had a "progression" some way or another?

Then there's these prog metal bands like Symphony X. They confuse the $h!t outta me. Mike Romeo rarely plays full "chords" in the songs but I can still hear the music rise and fall as though it was a "chord progression". Yet I am still told it is riffs BUT then people start telling me about Symphony X using "implied progressions and harmonies".

Someone explain, what makes a riff/melodic figure different from a progression? Even if the riff is harmonized like chords. What is "implied progression/harmony" and how do you do it?
I have a song that will explain this perfectly. Listen to Apollo I: The Writing Writer by Coheed and Cambria. Listen to the pre-chorus. Listen to the riffs. Now, listen to the next section (the chorus) They both use the same chord progression, only the progression is implied in the pre-chorus as little lines. So you feel the chord progression, but there are no chords being played, just melodic lines.