Q. If you are a salaried employee, and you want to take time off, do you have to use your sick or vacation days?
A. The basics of the work contract is people are paid to come to work, and to deliver results. For most employers, when an employee does not come to work, or deliver results, they are not paid. You don't say what you need or want time off for, but it does matter to many employers, and the reason may make you eligible for FMLA (family and medical leave act).
Depending on your situation, your employer and your manager, there are a few other ways to get time off from work. As a salaried employee, your work week is not defined hourly, and does not include overtime. Most salaried employees are provided with vacation time, sick time, and perhaps personal days so they can take time off from the job.
Your seniority, your role, and the culture of your company will also determine whether you will be able to take "comp" time which is compensatory time for hours over the norm which you worked, and can take as time off to make up for the over-time.
I have also seen situations where employees have asked for time off without pay. Perhaps they want to take an extreme vacation, or some kind of sabbatical. Employees still carry costs, even though they may not be collecting a check for a specific time period. These can be made possible through things like health benefits, or other areas of financial contribution. But be prepared, because although some employers may agree to time off, others will not.
People need time off for a wide range of of reasons such as caring for family, attending parent-teacher meetings, mental health days, etc. Employers provide a wide range and of ways to get time off, so you do have many ways to take time from work, with pay and without.