Execution time with warm up cache
If the reporter had any thoughts of rigor I would expect the hot cache / cold cache information to be included in the report. Otherwise it is like saying a car costs $y without saying which option, warranty, service or taxes that includes. Similarly I would expect to see it stated that subsequent tests were performed under the same conditions and how that was achieved. In less formal discussion I would assume hot cache, as that is the usual operating condition, unless told otherwise.

The two conditions emphasise different aspects of the host configuration. For a cold cache one sees more of an impact from the disk subsystem. For hot cache it is more about memory pressure and efficiency of the query plan. It would be unusual to find a workload that was purely one or the other in a real-world scenario, however.

SQL Server, for one, assumes a cold cache when costing a query plan.