Why moisture is the whole story
Freshly cut wood can be around half water by weight. Burning it spends much of the fuel's energy boiling that water off, which means less heat in the room and much cooler flue gases.
Cool flue gases condense on the flue wall, and that is exactly how creosote forms. Wet wood is the single biggest cause of the deposits that lead to chimney fires.
How to tell if it is actually seasoned
Seasoned wood is lighter than it looks, has cracks radiating from the end grain, sounds sharp rather than dull when two pieces are knocked together, and has bark that comes away easily.
A moisture meter on a freshly split face is the only definitive test. Aim for around twenty percent or below. Meters are inexpensive and settle arguments with suppliers quickly.
Buying without getting caught
"Seasoned" is not a regulated term. Wood sold in autumn was often cut that spring, which is not long enough for most hardwood. Buying a year ahead and stacking it yourself is the reliable approach.
Buy by the full cord and understand the stacked dimensions you are agreeing to, rather than by the vague truckload.
Storing it properly
Stack off the ground with air moving through the pile, and cover the top only. A tarp wrapped down the sides traps moisture and undoes the drying.
Keep the stack away from the house foundation to avoid inviting insects and rodents against the building.