These are the NOVA classifications, where processed and ultraprocessed are groups 3-4 respectively. These definitions have evolved over time [1], which means that it can be confusing to read different studies, when the formal definitions have changed after publication. So the best thing is to ignore the "ultraprocessed" category as a general term and instead read what the methodology was in any given study.
What researchers mostly don't do is lump all sorts of things into an undefined bucket of whatever processes and ingredients they think are unhealthy that day. This is what pop-sci media does, and may be what the podcast is railing does. But studies on ultraprocessed foods tend not to do this.