Is separation considered to be a measure of layoffs and quitting from firm's perspective?
"Separation" is a generic term indicating that the person no longer works at the firm, or more often the process by which the person's employment ends. It can refer to a resignation, a retirement, or a layoff or a discharge.
A "layoff" is an event where one or more workers have their employment ended by the company, because there is no work of the type that they had been doing available. It most often is used of multiple employees at the same time. It may imply that the firm will offer the former employees a chance to return to work if conditions change. It implies that individual fault was not the primary reason for the end of employment. However, the word is sometimes used when the employee was at fault, as a way to soften the description. In some industries, there are legal consequences to a layoff that do not apply to other kinds of termination of employment, generally additional benefits or protections for employees who have been laid off.
A "resignation" (or less formally "quitting" ) is a voluntary choice by the employee to leave a job, for any reason.
"Retirement" is a special sense of resignation. It implies that the employee has left the job because s/he is at the end of a career, and usually has been in that job for multiple years. Unless it is a "mandatory retirement" it is at the decision of the employee.
The terms "termination", "discharge", and "firing" all mean that the employer has decided to end the employment for some individual reason, often something judged to be the fault of the employee.