The point is that being terminated, as opposed to resigning, has implications for unemployment and other benefits. It therefore matters if an employer is free to simply interpret an arbitrary action or non-action as resignation.
Looking at Texas's site [1], they explicitly say if your employer asks for a resignation it counts as being fired. There are also a bunch of ways for quitting to be eligible (i.e. "Significant changes in hiring agreement").
[1]: https://www.twc.texas.gov/jobseekers/eligibility-benefit-amo...