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Can someone please explain me the difference between "either of" and "either..or" What is the difference between "either of" and "either.. or" in the following context? Or do they have same meaning?
There are two light bulbs.
Does the second statement mean that the person can turn on only ONE of the two light bulbs and not both?
"Either" is a determiner, pronoun, adverb or conjunction. In the examples along with 'of' it is a pronoun occurring prior to the noun(pronoun!) it replaces and keeps both the options open but does not allow the liberty to choose both at a time.
In sharp contrast to this, EITHER is an alternative coordinating conjunction proceeding a word or statement followed by the disjunctive OR to emphasize the possibility of choice.
Either come or write.
You may choose either of them (the options).
No, in none of your examples you're not allowed the privilege of lighting them both at a time. You are given a choice.
"Either" is used with alternatives. Because both of your sentences use it, both indicate that the person has a choice of one or the other but not both. The difference is purely in emphasis (separating out each object) and style.
Even without the "either" in the first sentence, though, the sentences would still mean the same thing. This is because "or" in English is generally taken to be mutually exclusive:
A person can turn on light bulb 1 or light bulb 2.
would most commonly be taken to mean that you could turn on one or the other (i.e., either), but not both.
Note that this is only true when given two options. You can easily say:
A person can turn on light bulb 1, light bulb 2, or light bulb 3.
to mean any one of the three, but "either" is limited to two choices. The appropriate replacement would be "one":
A person can turn on one of the three light bulbs.
Or you could use "any" to indicate one or more:
A person can turn on any of the three light bulbs.
Typically, "either ... or" specifies one or the other, but not both. Most online learning resources, such as this one, mistakenly imply that "either ... or" always means one and only one alternative between two choices, but that assertion is not borne out in practice.
For example, suppose my company has an opening for a managerial position. I have two employees who seem like they would do a good job in that role. So I might say:
Either Susie or Richard should get the promotion.
Since there is only one job, only one of those two (but not both) can get it. So here, "either ... or" represents a narrow, tight choice. But it could also be used less tightly; I could say:
Either Susie or Richard would be fine for the role.
Here, I'm not saying that only one and not the other would make a good manager. I'm saying they are both equally valid choices. So the exact meaning depends on context.
Nor is "either" restricted to just two alternatives. If there are more than two good candidates, I could tack on more "or"s:
Either Susie, or Richard, or Maria should get the promotion.
Alternatively, I could just use commas to separate the list, putting an "or" before the last name:
Either Susie, Richard, or Maria should get the promotion.
Whether between two alternatives or several, though, in most (though not all) contexts "either ... or" is exclusionary, meaning only one choice can be made.
"Either of" is looser. It means at least one, perhaps both. Suppose in trying to decide between two good employees, I think of examining their previous experience. I might ask:
Has either of them been a manager before?
It's entirely possible that one, both, or neither has been a manager before. If there were more than two candidates, I would say:
Has any of them been a manager before?
In an answer to an earlier question, @tchrist explains that "either" is sometimes exclusionary, and sometimes distributive. "Either ... or" tends toward the former, "either of" the latter.
