I've seen both uses of the Konjunktiv I: Es lebe der König and Lang lebe der König
They both seem to mean Long live the king though.
Is there a difference between them or are they interchangeable?
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The crucial point is, that you are stating a wish here.
Lang lebe König ...
is fine. It is universally applicable, even if the addressed king is already of advanced age.
Es lebe der König...
is a fixed phrase best matching a newly proclaimed king, since he just started being king. Es lebe König Heinrich adds clarity, that the transition to king-ness is addressed. Another use would be for a severly sick (wounded in battle, poisoned, etc.) person, to express, that you wish health. (Note, that both situations are also covered by Lang lebe...) For other situations the wish is not easily understood, since the person already lives.
The second phrase is therefore more appropriate for non-persons as love, democracy, tolerance, freedom etc., which don't really live, to show your sympathy.
Es lebe der König! = May the king live!
Lang lebe der König! = May the king live long! = Long live the king!
So, the meaning is quite the same.
About the grammar of both sentences:
Both sentences are imperative sentences, this is the mode for commands (»gehe fort« = »go away«) and wishes, as in you examples.
The word Es in the first sentence is an expletive pronoun. It is there just not to have the first position of the sentence being empty. In English there is one way to use expletive pronouns, like in this example:
It is raining.
This English it and the German es do not refer to the producer of the rain. They refer to nothing. Both words are here just to put something in position 1 of the sentence. If used this way, this expletive pronoun is the grammatical subject of the sentence, and there is nothing else in the sentence that could be the subject or that would name the actor/performer of the action.
But in German you can use this expletive pronoun even if there is a word (or group of words) that could be the subject or that is naming the actor/performer of the action:
Es ziehen Wolken über den Himmel. = Wolken ziehen über den Himmel.
Clouds are moving across the sky.
Es fährt ein Zug nach nirgendwo.(1) = Ein Zug fährt nach nirgendwo.
A train goes to nowhere.
(1) Title of a German Schlager from 1972
And with the same pattern, but now imperative instead of indicative:
Es lebe der König! = Der König lebe!
May the king live!
But you also can put an adverbial (adverbiale Bestimmung) on position 1 instead, and this is what happened in your other sentence. But this adverbial has a meaning (which »es« doesn't have), so it keeps existing in the sentence if you move the subject on position 1:
Lang lebe der König! = Der König lebe lang!
May the king live long!