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I am considering applying to other positions within my company. These positions are different from my current job but I ultimately aspire to work in one of said positions.

There are no internal protocols for informing current managers about applying to other jobs within the company. I am not sure if my manager will receive a notification that I've applied to a job. Should I tell my manager I am applying to these positions? I ask because I do not want to form a contentious relationship with my manager as the jobs I'm applying for are longshots.

Edit: Thank you for the replies everyone. After doing some more research I found the only stipulation is that I have to inform my manager if I am offered an interview for the position. This leads me to believe my manager is not informed upon applying. I've bolded the previously incorrect section for reference.

Should I tell my manager about applying to a different (internal) job?

Absolutely.

You definitely should tell your manager, and in most companies I have worked at you have to in order to apply for other openings. Even if there is no policy at you organization, most likely your manager will find out anyway so let them know so it doesn't look as though your trying to go behind their back.

I ask because I do not want to form a contentious relationship with my
manager as the jobs I'm applying for are longshots

I would consider this action very carefully as you don't have as much control here as you might think. Your manager may or may not react well to you not being happy with your current position. (or feeling the need to look elsewhere in the company)

While most managers would probably be okay with this, some will not. I am not sure I would be apply to openings that I most likely won't get and take that risk.

YMMV

Your manager will likely be called for a reference. You don't want that call to be a surprise. It could affect the reference.

Does your manager consider you a valued employee?

TLDR: If so, yes. If not, start looking for another job regardless.

The reason I'm asking is because at most places I've worked, the policy was that we'd rather lose a good employee to a different department then to a different company. In fact, applying for jobs internally was usually encouraged and seen as a positive thing, with internal applicants being preferred for any position.

It seems to me that most other answers assume your current manager will punish you for trying to leave, but have you considered they might reward you? Ideally they'll reward you with the job you want, but if not, at the very least you have signaled you are looking for more or a different challenge. This might be a reason for them to offer you incentives to stay (promotion, pay rise, more challenging work) or a different position in the company more in line with your ambitions. I've seen this happen lots of times, and was involved with hiring and promoting employees myself.

Smart managers know that failing to meet an employees ambition will ultimately cause them to leave, which is almost always a loss. Lots of companies adopt strategies to prevent this, with internal mobility as the number one tool at their disposal.

Of course this hinges on the question: Would the company want to keep you? Don't just assume they wouldn't, hiring 2 new people is more expensive than 1. Also, the fact that you're there presumably means you are of value to the company.

Lastly, consider that if you are in fact not deemed worthy to be kept on the payroll, you are probably not deemed worthy of promotion or pay rise either, and "go looking for another job" would be good advice to most people in your position.

Note: Other answers seem to be absolutely sure about the correct thing to do. Maybe it's country-specific, but from my experience in Europe there is no one-fits-all rule.

It depends.

If you're working in a small company where everybody knows everyone, then you should tell it to avoid the impression of going behind your manager's back. It won't stay secret anyway.

If working in a big company, then you should not tell, because it will backfire if you don't get the other job. The same rules apply as for external interviews. Your boss will lose you and probably never see you again. Why should s/he use the limited budget to invest into you? You've excluded yourself from any growth opportunities.

Of course there are exceptions and a big grey area.

Therefore you should try to get more information. For example casually talk to the guy who switched departments last month. You might also deduce something from following questions... Do the old and the new manager know each other? If yes, tell it. Is HR a black box and people question if they're actually working sometimes? If yes, don't tell. ...

Even though there are no internal protocols about it, you should still tell your manager about it. So he/she can plan ahead of time on what to do in order to fill the job that you will be leaving out. And I do think it wouldn't be a problem, because it is just a different internal job, not on a different company.