A trash-out, strictly, is the removal of debris and abandoned belongings from a vacant property so the space is empty. Furniture, mattresses, food in the fridge, whatever the last occupant left. It's normally priced per job by the volume you haul, which is why she asked for cubic yards, and the number usually includes your labor, your truck, and the dump fee.
Cleaning is a separate scope. Deep cleaning means scrubbing kitchens and baths, wiping cabinets inside and out, floors, windows, appliances, to the point where a property can be shown or moved into. Some clients bundle it into one price and some want two lines on the invoice. The loose market usage of "clean-out" covers both, and that's where you got crossed up. When someone says clean-out, ask them plainly whether they mean haul only, or haul plus clean.
The broom clean phrase you read is real but it's narrower than a deep clean. Broom clean means the debris is gone and the floors are swept. It does not mean the tub is scrubbed.
One thing to build in now: photograph the property before you touch anything, during, and after, room by room, including the exterior and any outbuilding. Banks, servicers and their agents nearly all require photo documentation to release payment, and if a former occupant later says something valuable went out in your truck, those photos are the only record you have. Handling of abandoned personal property is set by state law and sometimes by the eviction order, so ask the agent in writing what she wants done with anything that isn't obviously trash.