For short durations, can't we say operations management and project management are same (question based on respective definitions/characteristics)?

this is a mistake that some are making, a project is a project and has it's own characteristics regardless if it is a short duration project or not.

focus is become less while considering such project as operations and this is one the reasons why small project fails

Many people get confused between operation and a project, even though the difference between them is so clear. This is possibly because they share some characteristics, such as:

• Both are performed by people,
• Both are planned, executed and controlled, and
• Both have resource limitation

I dont think we can. Operations and projects are two different things and have different scopes and goals. Simply you may holt a project for the sake of operations but you can't do the reverse.

This is how most of the people use to consider. Both Project Management and operation management is different.

Project management is the techniques used to complete the given and particular assignement, where as operations management is vast it can be included for each and every task to complete.

Refer below 

Operations Management is an ongoing organizational function that performs activities to produce products or supply services.

In contrast, projects are temporary and help the business to meet organizational goals and to respond quickly and easily to the external environment. Organizations use projects to change operations, products and services to meet business need, gain competitive advantage and respond to new markets.

They are different. The project manager has the responsibility to deliver the project. After that the project is transferred into operation and then it is the role of operational manager.

Project is unique, temporary, with a defined purpose, and are almost always too complicated to be done in normal operations.

Operations is the opposite to project, they are continuous, routine tasks, that are boken up into defined tasks in their respective departments