Termination of Service is a broader term and dismissal is a way of doing it, the other one is Removal from service, both are as a result of disciplinary action and dismissal is extreme punishment and is imposed only in grave misconduct cases like theft, abuse, threatening, assault, dishonesty, fraud, etc and shall not be imposed in cases like absence from duty or found sleeping while on duty. It is said that dismissal is like a death sentence to a criminal and should be imposed only in the rarest of rare cases.
Discharge means discharge from contractual obligations and as per the employment contract, the employer can discharge an employee by giving notice of termination complying with the notice period regulation.