What is the best strategy to deal with these situations
Case A: Your manager asks you to do trivial and valueless tasks. He compares you with Jim who did a similar job but actually not the same.
Case B: When you think you deserve a promotion, your manager responds with, "Look, Jim works harder, but he wasn't promoted either".
I'd rather be able to deal with these situations more than simply "deal with it".
Be factual, not moralistic.
In case A, if it is not actually the same, establish objective criteria regarding why it is not the same. Is it more time consuming? More difficult? Avoidable somehow? Focus on those differences, so that Jim doing something becomes unimportant to the discussion.
In case B, try to get an objective criteria for promotion. "Working hard" is quite subjective. Ask your manager "What abilities or traits should I demonstrate in order to be promoted?". That way, this isn't about you or Jim anymore, it's about skills. Either you have them or you don't.
In both cases, avoid saying anything along the lines of "That's unfair!". It will sound immature and add nothing to your position.
Well these are two very different topics.
case A: your manager asks you to do a super trivial and no value tasks. He compares you with Jim who did a similar job but actually not the same.
You do the task because he is your manager and its your job to do assigned tasks, even if they might seem beneath you.
case B: when you think you deserve a promotion, your manager say, "look, Jim works harder, but he doesn't even get a promotion yet".
This is a version of the No True Scotsman fallacy. The implication is if you were a good team member(a true scotsman) then you would wait in line behind Jim. It also falls into the False Equivalence, Ignoratio elenchi, McNamara, and Appeal to self-evident truth fallacies.
Regardless the most effective way to handle this situation, is to get your manager to commit to some set of SMART goals that he needs to see from you to promote you to your desired position.
Your manager has already decided he is not promoting you right now. There is no argument you can make that you can also realistically expect a rational decision to change his mind. However if you can get him to commit to a promotion if you achieve some Specific, Measurable, Achievable, Relevant, Time bound goals then you know what the bar is to achieve your goal of being promoted.
It is also possible that you have some deficiencies that you will need to correct before he will be willing consider setting promotion goals. It seems like from his from his response he may feel that you are not committed enough, or working hard enough for a promotion. In this case you need to understand what his expectations are in this manner. I had a manager that expected vacation time to be used in chunks. I have always preferred to take long weekends with one week of my vacation. Many managers do not have a problem with this but my one manager did. Understanding her expectation allowed me to correct myself, and in the end I ended up with a good review. You need to understand what his measurement is. It could be he is looking around at who is still there at 5:15, and if you always leave at 5:10 (already 10 min over) he may think you are not committed. The best thing you can do for this is get him to set a measureable bar for you in this regard.
It is possible that you will find the goals far too onerous for you to bother trying to achieve them. In that case you will have to decide if you are content with your current position or if you need to find a place that will better align with what you are looking for.
If you feel that the comparisons are equating unequivalent tasks you just need to highlight how the situation is different and push for what you want.
"Yes Jim did apply labels to client folders and still managed his day to day duties however he had a week to do it and the labels were preprinted for him. I will not be able to do this in two days without support on my day to day duties."
or
"Yes Jim doesn't have a promotion yet however, hard work aside, we have different skill sets so there could be a promoted position for which I would fit that he wouldn't. For example my XYZ skills could be strongly leveraged in an ABC type role to really help the company. What do we need to do to get me into that sort of role?"
Stop worrying about Jim.
This is between you and your manager. You have to communicate your career goals, your manager has to manage you in such a way that these coincide with the company´s goals, if possible. If your manager starts comparing you, clearly state that this is about you and you want to discuss your opportunities not Jim´s.
You can also try to paraphrase for example
manager: Jim does X in only 2 hours
You: So I understand you want me to be able to perform X in under 2 hours? Sounds fair, I can do that.
If you want a promotion or a raise, always ground it on your own achievements, your personal development etc. If you are not satisfied, look for opportunities.
It´s always a better argument to say:
I could earn X if I work over there
than to say:
Jim earns X so I want that too.
It may be that you earn lower salary than Jim so manager assigns tasks according to this. For example, if you're playing in NBA for 20 million per year, you won't sit on the bench, no matter what's your accuracy or other stats.
It also may be that manager don't trust you or thinks you may be looking for other job. If you could prove that you can complete trivial tasks efficiently, maybe you could get more important assignments.
On the other hand, you should show initiative by yourself how to make bigger contribution to the company.
