Is Visa refusal the same as rejection?
No, a rejection is declared due issues outside of the applicants' control like
the applicant must meet an age requirement to apply on a route and they are not young or old enough
the applicant must have been in the UK/outside the UK when they made their application, and they were not
This is called a Validity rejection, this is not the same as a refusal and will not impact your file in any shape or form
An application can also be voided
An application is void when it where it would not be possible to grant the applicant the permission for which they applied. For example:
an application for limited leave to enter/remain (permission to enter/stay) made by a person who already has indefinite leave to enter or remain (settlement)
This also applies if the applicant dies before the application is adjudicated.
Is cancellation the same as Withdrawn?
Cancellation is the action of rendering an existing permission to stay/enter in the UK invalid
This is usually done when you make another application, but that can also be at all time.
The grounds for cancellation are laid out in Part 9 of the Immigration rules, are many and range from :
Making of false representations, submission of false documents or false information and failure to disclose relevant facts in relation to, or in support of an application
Change of job or lower salary rate
How is Visa Withdrawn(after the biometrics) treated, do they consider the withdrawn application for future applications?
If they suspect that you lied on your application or any other reasons , they can deny your withdrawal and still adjudicate your case
The most common reason to refuse to accept a withdrawal request from an applicant and decide an application is where there is a suspicion that deception has been exercised by the applicant. For example, if the applicant has knowingly submitted fraudulent documents.
In this case, the visa becomes refused and you must report a refused visa everywhere
Is it necessary to mention in future applications that one has previously withdrawn the application for any country(due to any reason)?
If your withdrawal is accepted, your application will not be adjudicated and it's very unlikely that you will have to mention the withdrawn application