This has been a hard concept to grasp for many managers I've come across in my career.
The only difference in the context of the warnings is how you document it and communicate it to the employee: Verbal or Written. Documentation of a verbal warning to an employee is generally more informal. Written warnings are usually more formal and most often are laid out in a designated format or on a designated form. The key here is not getting too hung up on the difference, but rather the fact that you are documenting all levels of disciplinary action for an employee. If they have a repeated violation of a policy, but it is not a severe violation, progressive action is usually taken, thus beginning with a verbal warning. For those violations that may be slightly more severe, a formal written warning is usually the first step. Violations that are gross misconduct or illegal are usually handled with more severe discipline and do not even need a verbal or written, but should still be documented.
Your company's policies should indicate what policy violations could result in progressive discipline (starting with verbal warnings) and what policy violations could result in more severe discipline (written warnings, suspension, termination). The key is document all levels of discipline so you have a paper trail of the employee's issues and what action the company took to correct the issues. This becomes especially important if the employee is ultimately terminated and files a claim(s) against the company.