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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 Masters, 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 improductive. I show initiative (or at least I belive 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 PI defensive, and make me appear like a negative person - which obvisouly 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 whould 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.

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

Based on your own judgement, is your contribution is much more significant than that of X? If no, then maybe your advisor is trying to balance the credits. You are the first author, but then X is allowed to present. Would you choose the other way round, i.e. to present the paper with X as the first author?

He asked X to review an article in his name

Not sure what do you mean by "in his name". But reviewing an article is often considered as an exercise to get familiar with the field. As you already worked on this topic in your Masters, X was the one who needed to do this exercise.

A collaborator suggested a new side project that would quickly and
easily lead to a paper.

At the end of the day, your advisor needed to make a choice. If he chose you, perhaps perhaps it were X to ask this question. Maybe the next opportunity is your turn. Maybe you are closer to your own paper, and your advisor wants you to focus on your own project. I would not too fast to jump on the conclusion that your advisor favors X. From what you have described, I do not see any problem with the advisor-advisee relationship. It seems to me that you just overthink it.

I would at least bring it up since it is on your mind. But I would not escalate it to an ultimatum. The story rings true and I have seen similar. Some people you need to at let them know the objection or they continue to walk on you. But again, I would not expect satisfaction. But at least get it off your chest and get the guy on notice.

Oh...and take care of yourself on papers going forward (take first author, write stuff up before discussion, etc.) Continue to include X and the advisor, but stay in front on the papers. Most important thing. Oh...and finish up and get out of there ASAP. Sounds like you are a self sufficient as a researcher and the relationship is turning competitive.