It seems my advisor doesn't trust me, but why? Even though my advisor is reasonably friendly with me, it feels like he doesn't 'trust me' as much as he trusts the other grad student (let's call him X) in the lab. A few examples:


I joined a lab a few weeks before X and we both worked on the same project until recently, and both made significant contributions to the project - but I was first author on the paper. Without telling me, my advisor asked X, the second listed author, to present our work at a local conference, instead of simply asking us both who would be available. I did not even know about it until X asked me to review his presentation.
He asked X to review an article in his name, about something that I know more about: the manuscript is focusing on something very similar to what I was working on during my Master's, whereas X is unfamiliar with some fairly important notions in this sub-field. One again, I learned about it by chance.
Both X and I have moved on to different projects now, and are both working full time on these. A collaborator suggested a new side project that would quickly and easily lead to a paper. Guess who was offered the opportunity to join that project (despite not having more relevant experience)? That's right: X again.


I don't think I mentioned anything along the lines of "I have so much work I can't do anything more" but I also don't think I came out as idle or unproductive. I show initiative (or at least I believe I do) so I really have no I idea why I'm not given these opportunities to learn and/or build an academic record. 

I'm afraid that asking if something is wrong would make my advisor defensive, and make me appear like a negative person - which obviously does not help. But if I'm doing something wrong (or not sending the right signals, or anything like that) I have no idea what, and I would like to fix it as soon as possible. 

Any idea about how to approach this issue diplomatically?
You may be misinterpreting and actually getting it backwards. Of course, I don't know the prof or the other interactions, but much of what you write here could well be explained by your advisor trusting you completely to get it right and the other student needing more help and practice to get up to where you are. 

Student X may need all the help they can get, whereas you are trusted to make it without the need for extra intervention. It could also be that some people know you already have enough to do. 

I could be wrong, of course. 

But it would be worth having a face to face conversation asking your advisor for advice on your progress and, especially, any advice on what to do to position yourself for a great career. I'll guess that if there are any reservations about you that they would become obvious in such a conversation without having to directly ask whether you are trusted or not. And if you are trusted, the advice would probably be pretty valuable in the future.