You need to keep in mind that verbs never refer to future events in English - they always see the event from the standpoint of the present. The present continous describes an on-going temporary event happening around the present moment - the event has started, not yet finished, but there is a predictable end. So for example : Where's John? / He's working in Rome this week.
The event started on Monday, it's now Wednesday and the end is predicted for Friday. You could represent it with this timeline :
where A is the start of the action (Monday), B is the present moment (Wednesday) and C is the predicted end (Friday). (Contrast this with He works in Rome
which has no predicted end)
When I say I'm meeting John next Friday
, it's actually the same thing. For English grammar, an event starts when it's arranged. So - A (the start of the event) is the moment I made the appointment, B is the moment of speaking and C (the end of the event) is the actual meeting with John on Friday. The verb expresses the present situation - a meeting with John is on-going in the sense of being arranged but not yet completed.
and be going to
, which both express the concepts of prediction and volition but in different ways, see two articles here
I don't completely agree with Clive when he says :
1.I'm going to play squash with Alex next week.
2.I'm playing squash with Alex on Friday at 15.00
For me (1.) this means that you have the intention to do it, although nothing has been confirmed.
(2.) on the other hand means that you've booked the court and this appointment is confirmed.
If you have the intention of doing something, and then make a firm arrangement, it doesn't mean that you no longer have the intention. In this case, the event is both an intention and an arrangement. So you could use either, depending on how you wanted to present it - or what you wanted to "mean"