What's the difference between 3/4 time and 6/8?

Nick was asked how to play a song in 3/4 time and what the difference between 3/4 and 6/8 is. Here he shows how to play in these time signatures and how to identify the differences.

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Abridged Script:
My thanks to Roger in El Paso, Texas for a question about playing a song in ¾ time. The song in question is a Christian Praise song called ‘Great are you Lord’ sung by American duo All Sons and Daughters.
The bulk of the song is a repeated 8 bar sequence played something like this… Here are the chords I am playing.
Now these are nice substitute chords that I picked up from a YouTube lesson that Roger sent me a link to.
But as this is a lesson about strumming, unless you find these chords easy to change quickly between, I am going to suggest you start by using the plain vanilla chords: C Em D D. That way, you can put all your attention on the rhythmic aspects of the strumming pattern.
The YouTube lesson I looked at on this song is great, but it contains one piece of misinformation right at the start of the lesson when the presenter tells you the song is in ¾ time.
Songs in ¾ are usually quite easy to differentiate – their main pulse has a strong feel of being divided by three 123 123 123 with a relatively heavy emphasis on the first beat.
On the guitar, the best way I know of to be certain that you are playing in ¾ time is to play the strong first beat as a bass note and the two weaker beats as strummed chords. So here I am showing this for a basic open C chord. You can see that we are dividing six beats into two identical bars or measures.
1 2 3 1 2 3. A good reference for this is to think of a waltz bass line played on a tuba or sousaphone – oom pah pah oom pah pah
By contrast if we took these two bars of ¾ and converted them to one bar of 6/8 we would need to smooth the rhythm out …and the best way I know to do that on guitar is to reverse the pattern so that we are strumming the first and fourth beats and playing lightly sounded bass notes on beats 2,3,5&6
123456 123456 notice that instead of a predominant 3-beat feel that we get with the ¾ pattern 123 123… we now get more of a two-beat feel. This is why, my preferred way of counting in 6/8 is 1 & a 2 & a …
So that is the basic difference between ¾ and 6/8 – one has a three beat pulse, 123 123… - the other a smoother 2-beat pulse 1&a2&a
Now back to this song. I advise starting by playing the basic 6/8 pattern I just described over the simplified chords like this C Em D D – call that step one.
Do this for an hour or more if necessary, until it feels natural and sound smooth.
You can always double or halve beats in music without affecting the time signature, so the next step might be to double up on the 2nd and 5th beats of each bar like this 1 2&3 4 5&6 and on the 3rd and 6th beats as well 1 2&3& 4 5&6&
Once you have found a pattern that flows nicely for you and that you feel is appropriate for the song then practice that pattern until it becomes second nature.
Then see if you can use this pattern over the slightly more difficult chords that we showed you at the start of this video.
There are quite a few songs out there is 6/8 time so this approach should come in useful for all guitar players who want to improve their rhythm playing abilities.
My thanks again to Roger for raising the question and I hope this advice helps you crack the problems you were having with this particular song.