Actually, there isn't sufficient data to give you the right inputs, and all that has been said earlier are a few dimensions. If it is a sole trading business, you may not get an appointment letter, or if you are working for someone who is, say, in the cracker manufacturing business in Sivakasi, then too there are chances of you not getting an appointment letter because even the one who employs and pays your salary isn't sure of his business.
Hence, it would have been nice to know the nature of the business or the place you work, and the number of people working.
Using the Normal Practice
As one who could be launching into a career as a new employee, appointment letter issues are far from your mind. Like most people, you want to get started, and you are thrilled that you are starting a new phase in your life. You have a job. You are full of eagerness and expectation.
After a while, when the enthusiasm has subsided somehow, you realize that you do not have an appointment letter. You do not know most of the terms and conditions of employment or how you know terms and conditions of employment. And you are not very sure what you need to do. You inquire from your working colleagues about the issuance of appointment letters.
Management may not have issued appointment letters to some of them when they first reported for duty. They tell you they have their appointment letters now. This assures you, and you wait a little longer. A month passes. Then two months. No appointment letter. What must you do? Must you wait some more?
This is the dilemma because if you want to take up another job to further your career, you will have no proof whatsoever. You'd have to start all over again as a "fresher." Then what would you mention on your CV, "working and have experience" or "not working and no experience"? This then reduces the chances of your job prospecting.
The most reasonable thing you can do is to see your supervisor. He or she is supposed to help solve any subordinate's problems. If your supervisor has no answer to your inquiries, then he or she should either refer the case to the one who is heading Human Resources (HR). Do not by any means bypass your supervisor by going to the Head, HR without his or her knowledge or permission. This is not right based on the reporting channel.
Having waited for this long, you may need to wait a little more if your employer gives a reason that seems acceptable. But do not wait any longer than one month. Find the first opportunity to see your supervisor or alternatively the Head, HR people after consulting your supervisor.
The Issue
You are told that you will get the appointment letter at the end of the probationary period. This is a real appointment letter issue.
My Submission
This is not proper. At the end of the probationary period, your employer is supposed to issue you a confirmation letter if your work is found satisfactory.
Contents of the offer letter differ from the appointment letter. This amounts to a lie on the part of the employer. This is another reason why an offer letter is not necessary.
This is an assumption: Only senior employees are issued appointment letters. There is no acceptable reason for doing this.
However, lastly, you are free to ask for permission to see the right people if not in HR, someone higher up regarding your problem.
Having said this, I'm surprised that there are such nomad organizations still on the face of this planet. It is only right that employers issue appointment letters to new employees before they report for duty. They could claim to have some valid reasons for this; however, it is not the norm. It is not proper; it's unethical, illegal.
Have patience, do not do anything in a hurry to hamper your entire career. Who knows, this roughing out could make you an entrepreneur who will want to set an example of being a good employer in the future.