Currently, I am looking for a job. Or am I looking for a job opportunity? Or is the hiring company having a job opportunity for people like me?
Can I use "I am looking for a job/job opportunity" interchangeably, or is there a difference?
You are looking for a job.
I don't think you would be satisfied with just a "job opportunity". If you were offered a "job opportunity", you would want to follow through until you either got the job, or did not get the job.
Similarly, a child who wants to pet a cat does not want a "Schrödinger's cat", because Shrödinger's cat has a 50% chance of being dead when the child tries to pet it. The child wants a real, live "cat".
You are looking for a job. However, in order to find one, you will have to look for job opportunities and apply to them.
Perhaps you will search job adverts for potential job opportunities, or recruiters and hiring managers may tell you about job opportunities that they have. This is because they are offering you the opportunity to apply for the job (they are not offering you the job yet).
A job opportunity has the potential to turn into a real job. If you apply to a job, get invited to interview and are successful, then you will be offered the job.
So, if you are talking specifically about the process, you might say that you are looking for job opportunities, but if you are talking in general, you say that you are looking for a job, because that is your end goal.
It's a false dichotomy; you are looking for both, and either is idiomatically correct after "I am looking for a ...".
It's similar to if you were going shopping for shoes. Are you looking for a shoes, or are you looking for a shoe shop? Well shoes don't lie around in the middle of the street (well, not any that you'd like to wear I assume), so strictly speaking the actual aim of the search, initially at least, is to find a shoe shop. Shoes live inside the shoe shops and you're not going to get the former without first getting the latter. But clearly the end target is the shoes, because ... , well, you can't wear a shoe shop.
In the same way, although your ultimate aim is a job, jobs don't sit around waiting for you to take them. Job opportunities, do. And jobs live behind those opportunities. Even if someone grabs you in the street and says "Neftas! We need you to take this job right now!!", it's not a job until you've signed the deal. Any salesperson will be very sensitive to that distinction.
Another analogy is travel. If you're going from San Diego to London via New York, and someone asks you as you enter at SD "Where are you going, New York or London", the answer is that you are going to both.
Actually, idiomatically it's possible for there to be a very subtle usage distinction between the two. Compare:
The first would usually imply that you are looking at a job from a current state of unemployment. The second would be more likely to be taken to mean that you are open to taking other jobs, but that you already have one. More precisely, the first implies a greater need on your part than the second, and so for sales-tactical reasons, although both are strictly true, the second approach may be better. In the same light, just for completeness, the following:
would mean that you currently have a job but are in some way not satisfied with it and so are actively hunting out a new one.
The phrase "Job opportunity" is used by recruiters when they are trying to convince you to apply for a job. They are trying to convey a feeling that this is a rare "opportunity" that you should snatch quickly, otherwise you will regret for the rest of your life.