Emergency lighting has a number of different purposes in a building, of which three are commonly used:
1) Escape lighting - providing sufficient levels of light along an escape route so that a person can safely navigate their way to safety should the normal lighting fail
2) Emergency safety lighting - providing sufficient levels of light in an area of high risk so that a person will not sustain injury if the normal lighting fails (e.g. lift machine rooms)
3) Emergency lighting of safety features - providing sufficient levels of light so that safety & warning signs, fire extinguishers, fire alarm break points, etc can be identified and used should the normal lighting fail.
The "exit box" or internally illuminated exit sign is one way of achieving element (3) of an emergency lighting system, however by design are not intended in themselves to contribute to element (1), the illumination of an escape route.
Both scenarios (1) & (2) in the original post are types of exit box - you can either go for the purpose made unit with the transparent cover incorporating the legend or use a self adhesive legend on a normal emergency luminaire - cost & aesthetics usually determine which is used.
Signs and lights are not seperate, it's the purpose for which you are using the lights that is the key.
You may need escape lighting and thus place units to meet the light & placement requirements (a certain amount of lux of illumination for a particular type of space with specific cover for stairs, junctions, etc).
You then need to decide if the escape lighting units will provide the required level of illumination of your exit signage - if so, you can use normal signs and the task is over. If not you can either:
a- add additional luminaires adjacent to your signage
b- install "exit boxes"
c- if continuously exposed to a suitable light source to 'charge' them up use photoluminescent signs
Of course in some premises the use of the "exit box" was a requirement of legislation (cinemas, theatres, licensed premises, etc) and had to be provided in addition to other emergency lighting.
The illuminated sign/exit box is therefore a type of emergency light to fulfil a particular requirement of the British Standard as well as in particular codes