Can Staff be categorised as a grade - procedure I'm following is correct or not?

I am coming with an issue in regard to grade of employees.The organisation I joined is marking employees under executive,serior exe,staff,asst.manager,manager and sr.manager.But what I noticed is that particular grade is not fixed with particular range of salary.for eg: few executives drawing more than asst manager again in some case asst manager more than manager, some sr.executives are drawing below executive range. After I joined I changed the grade and kept a salary range based on grade,such as:
Exe:10-15
Sr.Exe-15.5-20,in this way.
According to my knowledge, grade is based on experience and efficiency at times.
Want all of your view in regard to the same and the procedure I'm following is correct or not?
Further can Staff be categorised as a grade?

You must be referring to the Salary Grade of jobs or positions within a company's Salary Structure.

The words "executive, senior executive, manager, assistant manager, and senior manager" are JOB TITLES and Job Classes that are apparently mixed up by your company. They are NOT job grades.

Job Grades refer to the hierarchy being used by companies in their salary structure. Job Grades may use numbers and/ or letters to represent the distinction between and among them. It is important in making sure that the salary rate ranges given to jobs do not result to distortion, i.e. the situation wherein small jobs are able to get higher salaries than bigger jobs.

In compensation, job grades can be correctly determined thru the use of Job Evaluation (JE). JE is the method used to determine the relative size of jobs within a company. Big jobs are usually given higher job grades while smaller jobs are given lower job grades.