There are actually two different Greek words being used here, which perhaps guides us to interpret the contexts differently.
At the Wedding at Cana, Jesus uses the word ὥρα (ōra), from which comes our English word "hour". The understanding by some in antiquity was that here Jesus was speaking of specific events in his ministry that had a particular time - or hour (as in, of a day) - and place reserved for them. An interpretation of Jesus' response at the Wedding at Cana is that it was not yet appropriate for him to begin the miracles he was to do, since this was very early - before even the Apostles were called.
John Chrysostom (4th c.) wrote:
When the mother of Jesus says, They have no wine, Christ replies, Woman, what have I to do with thee? Mine, hour is not yet come ...
The words are not used in this place only, but in others also; for the same Evangelist says, They could not lay hands on Him, because His hour (ὥρα) was not yet come (John 8:20); and again, No man laid hands on Him, because His hour (ὥρα) was not yet come (7:30); and again, The hour (ὥρα) is come, glorify Thy Son. (John 17:1). What then do the words mean? I have brought together more instances, that I may give one explanation of all. And what is that explanation? Christ did not say, Mine hour is not yet come, as being subject to the necessity of seasons, or the observance of an “hour”; how can He be so, who is Maker of seasons, and Creator of the times and the ages? To what else then did He allude? He desires to show this; that He works all things at their convenient season, not doing all at once; because a kind of confusion and disorder would have ensued.1
In John 7:6, however, John uses a much less common word, καιρός (kairos). Lexicons assign the meaning of something like "season" or "occasion" or "appointed time" to this word.2 John only uses this word three times in his Gospel account, including the one you cite, and only in one other place in the context of Jesus' time (two verses later, in John 7:8).
The understanding in antiquity here is that John uses καιρός, as it relates to Christ, in the Gospel to refer specifically to the Crucifixion, Death, and Resurrection. John will use the same word in the Book of Revelation in the context of Christ's Second Coming and the Final Judgment (e.g. Revelation 1:3;11:18;22:10) Chrysostom explains here:
He here seems to me to hint at something other than what He expresses; perhaps in their envy they designed to deliver Him up to the Jews; and pointing out this to them, He says, My time is not yet come, that is, "the time of the Cross and the Death, why then hasten ye to slay Me before the time?”
But your time is always ready
As though He had said, “Even though you remain with the Jews, they will not slay you who desire the same things with them; but Me they will straightway wish to kill. So that it is ever your time to be with them without danger, but My time is when the season of the Cross is at hand, when I must die.3
(In John 7:6, John is speaking not of the disciples, but rather those who did not believe; cf. John 7:5).
1. Homily XXII on John (tr. from Greek, Nicene and Post-Nicene Fathers, Series 2)
2. See, e.g., Newman, A Concise Greek-English Dictionary of the New Testament (Deutsche Bibelgesellschaft, 1993)
3. Homily XLVIII on John (op. cit.)