When organizations of similar size, states, or armies liaise, I have seen "counterpart" used quite often.
Example ; ...said Navy Capt.
John Kirby, spokesman for the top U.S. military officer, Adm. Mike Mullen, who spoke briefly by phone on Monday and Wednesday with his counterpart in Cairo, Army Lt.
Gen. Sami Enan.
obviously, it's only usable in that limited context of two structures/organizations interacting (as @Dour points out it can not be used to describe two equal-ranking colleagues on the "same side"), so it may not be what you are looking for.
english.stackexchange.com/users/239/Pekka
Although it isn't a word I've often used, I believe compeer is the word you might be looking for.
Defined as: a person of the same rank or status; equal; peer.
It is the best I think you will find, unless you just go with one of the above answers which do makes sense.
english.stackexchange.com/users/4631/LizzybethQ
My Webster's lists the following synonyms for colleague : coworker, fellow worker, workmate, teammate, associate, partner, collaborator, ally, confederate.
None of these really work in the sense you're looking for, something that means "in exactly the same job" as you.
If no one strikes gold for you here, I would suggest that one alternative for you is to be more specific about the actual job function:
My wife is a periodontist, just like me.
Jean and Kate were both trial lawyers.
Here are a few traits I share with my fellow QA consultants at IBM: [List]
Ed and Bill
and I have a lot of disagreements, but we're all teamsters and we stick together.
english.stackexchange.com/users/2303/Robusto
I think the word you're looking for is confrere
It comes from the French, and is masculine.
The feminine equivalent (in French) is consoeur though, in certain contexts you could also use guildsman, union-worker These last two terms refer to another person of the same job-class.
Though not colleagues, there is still an implied federation (that I think you were trying to avoid).
The question is also a bit of a repeat
english.stackexchange.com/users/23834/New Alexandria
The meaning of colleague is a person with whom one works, especially in a profession or business .
Even if there isn't any reference to the working place, the word is used when two people have contacts.
The meaning coworker is fellow worker ; looking at the meaning of fellow , on the NOAD
I read the following definition:
informal a man or boy:
he was an extremely obliging fellow .
•
a boyfriend or lover:
has she got a fellow ?
(usu. fellows)
a person in the same position, involved in the same activity, or otherwise associated with another: he was learning with a rapidity unique among his fellows .
•
a thing of the same kind as or otherwise associated with another: the page has been torn away from its fellows .
a member of a learned society: he was elected a fellow of the Geological Society .
• (also research fellow)
a student or graduate receiving a fellowship for a period of research. • Brit.
an incorporated senior member of a college: a tutorial fellow . • a member of the governing body in some universities.
I would use fellow worker to mean a worker involved in the same activity .
english.stackexchange.com/users/252/kiamlaluno
Colleague has the meaning you're looking for when the speaker is a member of a licensed profession (doctor, lawyer, that sort of thing).
Copractitioner may be slightly preferable to your fellow-X construction sometimes.
english.stackexchange.com/users/4526/chaos
Counterpart means someone who does the same job in a different location but you could extend it to different part of the same organisation.
english.stackexchange.com/users/53812/user2617804
Is there a word that means something like "someone who does the same job as me"?  I've thought of  colleague  and  co-worker .  These both indicate that someone works at the same place, or some other kind of work relationship, but they don't indicate that the job is the same.  The best I've come up with is  my fellow-X , but this feels cumbersome.
Word for "someone who does the same job as me"
english.stackexchange.com
<single-word-requests><terminology><vocabulary><expression-requests>
english.stackexchange.com/questions/11458
english.stackexchange.com/users/1926/lonesomeday
There does not seem to be an agreed term for someone who performs the same job as you but not necessarily at the same place. However, the term "counterpart" is used when organisations liaise with each other in this sense. Other possible options include "compeer" "confrere" or "copractitioner". It may be that you will need to be more specific about the actual job function. "Counterpart" is the term suggested to indicate someone doing the same job, but in a different location. Another term, from French, is "compere"  whilst others suggest "confrere" with the feminine "consoeur". This term does not mean colleagues but an implied federation.  "Colleague" is another suggestion or "coworker". Again, cCopractitioner  may be slightly preferable to the initial "fellow-X"  construction sometimes. The Webster dictionary provides numerous synonyms, some of which are suggested here, but none seem to represent the person doing the same job as the other.
There does not seem to be an agreed term for someone who performs the same job as you but not necessarily at the same place. However, the term "counterpart" is used when organisations liaise with each other in this sense. Other possible options include "compeer" "confrere" or "copractitioner". It may be that you will need to be more specific about the actual job function. Counterpart' can be used for someone with the same job, although it often implies the same role in a different company or department. As you say, 'colleague' does not necessarily mean someone with the same position. Other possible terms in different contexts include co-worker, co-practiotioner, associate, workmate, partner, collaborator, confrere or consoeur.
Compeer, or confrere can be used to describe someone who does the same job. A Colleague could be used if in a licensed profession, A counterpart means doing the same job in a different location, or different part of the organisation. Other possible words are fellow worker or copractitioner.   There is no exact answer to this question, but potential terms include "compeer", "confrere", "fellow worker", "colleague", "copractitioner" or "counterpart".
Counterpart Compeer Webster synonyms Confrere Colleague S1: Copractitioner  may be slightly preferable to your  fellow-X  construction sometimes.
Counterpart' can be used for someone with the same job, although it often implies the same role in a different company or department. As you say, 'colleague' does not necessarily mean someone with the same position. Other possible terms in different contexts include co-worker, co-practiotioner, associate, workmate, partner, collaborator, confrere or consoeur.
There is no exact answer to this question, but potential terms include "compeer", "confrere", "fellow worker", "colleague", "copractitioner" or "counterpart".