In John 14:27, what difference (if any) is there between "Peace" which Jesus said He gave, and "My peace" which He said He leaves, or is He talking about the same peace, just emphasising by repetition?
"Peace I leave with you; my peace I give to you. Not as the world gives do I give to you. Let not your hearts be troubled, neither let them be afraid." - John 14:27 (NIV)
Great question: is this a contrast, or a parallel?
Given the context of the passage, Jesus is concluding his preparations for the disciples ahead of his departure: in the previous verse he says the Father will send the Holy Spirit, now he himself will 'leave peace', and he also says he will 'give his peace'. However, he does not dwell on this subject for longer than a few words, and then moves on - so what did he mean?
Hermeneutically, we're often best taking the simplest reading of the text that we have in front of us. Here, if Jesus were trying to communicate two separate peaces, we would expect him to clarify that somewhat, or explain something of a difference between them. We might expect a κἀγώ (also), or at least a καί (and), or some other qualifier to explain that there is a difference between how he has used the word 'peace'. Given no such qualifier, we should read the passage assuming the two word uses are parallels.
But why repeat it?
If we assume this is a parallel, why then is it here at all? Is Jesus just saying the same thing twice so that the disciples don't miss it, or is there more going on?
The second half of the verse takes a deliberate attempt at explaining more about the peace: 'my peace I give to you - not as the world gives do I give to you'. To me, Jesus is trying to explain the how of this supernatural peace-delivery:
I leave you peace
I give you my peace
Not like the world gives, I give it to you.
Paraphrase: 'Yes, the Father is going to send the Holy Spirit - eventually. But before the Father sends him, I give you peace, peace of my own, not like the world gives things, I give it to you.'
Parallels in Scripture
The text is constructed/recorded in such a way as to clarify that Jesus is certainly leaving them peace - his peace - here and now. It's not the Holy Spirit, who the Father (not the Son) will send, it's not the sort of gift which the world gives, but it's a special and specific gift from him. The concept sounds similar to something Jesus told them when he sent them out to preach:
"If the home [you enter] is deserving, let your peace rest on it; if it is not, let your peace return to you." - Matthew 10:13
"If someone who promotes peace is there, your peace will rest on them; if not, it will return to you." - Luke 10:6
For Jesus and the disciples, there was a known concept of having your peace which would rest in places where you were welcomed as you travelled, and this is the sort of peace which Jesus is choosing to leave, as they would when they stayed in any household. Yes, the Holy Spirit is coming soon, but Jesus' peace will remain on the disciples.
Theologically there must then be a few ways this 'peace' could be understood, but that's out of scope for this specific question.