How does the verb 'save' contrast with its synonyms?
Some common synonyms of save are deliver, ransom, reclaim, redeem, and rescue. While all these words mean "to set free from confinement or danger," save may replace any of the foregoing terms; it may further imply a preserving or maintaining for usefulness or continued existence.
// an operation that saved my life
When could 'rescue' be used to replace 'save'?
The synonyms rescue and save are sometimes interchangeable, but rescue implies freeing from imminent danger by prompt or vigorous action.
// rescued the crew of a sinking ship
When would 'redeem' be a good substitute for 'save'?
While in some cases nearly identical to save, redeem implies releasing from bondage or penalties by giving what is demanded or necessary.
// job training designed to redeem school dropouts from chronic unemployment
I suppose conserve would be a more correct (or at least less ambiguous) term for what's meant.
But as I said in the comment, "Save me!" is a bit funnier and draws your attention as it personifies the electricity (or the light switch) a little, like it's asking for your help as well as asking you to save electricity.
Save me is fine because it does not necessarily only mean to save something or someone from something.
If you look at the Oxford Dictionaries Online definitions for save, you'll see five definitions including the following:
Keep safe or rescue (someone or something) from harm or danger.
- ‘they brought him in to help save the club from bankruptcy’
The definition above fits the save from context
The definition relevant to the save electricity context is actually:
Preserve (something) by not expending or using it.
- ‘save your strength till later’