Operating temperature (range) usually means the range of temperatures over which a unit or component has to 1) work and 2) meet all of it's performance parameters. This can be fairly narrow temperature range, 10 deg C to 25 deg C, or a much wider temperature range.
Integrated circuits, for instance, usually come in 3 temperature ranges - Commercial: 0 ° to 70 °C; Industrial: −40 ° to 85 °C; and Military: −55 ° to 125 °C. A component is guaranteed to meet all the performance numbers specified in the data sheet for the specified temperature range. These are all considered "operating" temperature ranges.
When it comes to systems, the situation is usually a bit different. Even for military systems such as airborn radars, the operating temperature is usually more limited than the full mil temp range for parts. -10 deg C to +65 deg C might be a typical operating temperature range for such a system.
The operating temperature range is usually specified by the specification/requirements document for the system.
In this area, ambient and operating temperatures are usually synonymous, as it doesn't make much sense to differentiate between the two. If I have an assembly that is going to be cooled by air being blown through the chassis, the temperature range of that air (the ambient) is the operating temperature range for that assembly. Similarly, if I have an assembly that is going to be be cooled by conduction and bolted to a heat sink of some sort, the temperature of that heat sink is the ambient temperature for that assembly, and also is the operating temperature range.
Now just because you might have a relatively benign operating temperature range for your assembly does not mean that the temperature range for internal boards and components on boards is the same benign range. In almost all cases, the board/components is going to be operating at a higher temperature than the external environment.
Take the earlier example of an assembly mounted to a heat sink. Say that the maximum temperature of that heat sink is 65 deg C. There might be a 10 deg C temperature rise from that heat sink interface to a place inside the chassis. Then there might be another 10 deg C rise from the chassis to the board, and another 10 deg C rise across the board to some component. So that component, an amplifier lets say, needs to be able to operate up to (65+10+10+10)=95 deg C. So we see that the operating temp range for a part (like our amplifier) is usually much wider than the operating (ambient) temp range for the assembly.
Also, just stumbled upon this old post: Ambient temperature vs operating temperature?