Is Offer And Appointment Letter Are Same ?

Sir,
I have resigned and given one month's notice to company but company wants me to continue my service till 2 months notice period as per the Offer letter.
Company is also not ready to give me resignation acceptance and neither approving my 1 month relieving date.
Is this really true that company can take legal action against the employee if they do not serve complete notice ?
I am ready to pay Notice pay penalty.
Please advice and let me know what all precautions i have to take.
Regards
Amit

DA Terms & Conditions are mentioned in appointment letter not in offer letter.
Regards,
Sujayalakshmi S

@ Chechi
Please refer the below links , to clarify your doubt
Letter of Intent
Letter of intent - Wikipedia, the free encyclopedia
Letter of offer
Definition:
A job offer letter is a document that confirms the details of an offer of employment. The job offer letter includes details such as job description, reporting relationship, salary, bonus potential. benefits, vacation allotment, and more. The job offer letter generally confirms the terms the employer and the
candidate have agreed to for his employment during negotiations.
Regards
Sriram
sriramwarrier@gmail.com