Es sind nicht alle gleich.
I understand this sentence to mean, “Not everyone’s the same”, but what is the es in aid of?
Would the following have the same meaning?
Alle sind nicht gleich.
The linked duplicate question does not help me as the es in that is raining, but the es in my sentence doesn’t seem to have a verb or anything attached to it.
You have stumbled across the use of es as a syntactical expletive.
German sentences (main clauses only; within the context of this answer unless otherwise mentioned) are split into three parts by their included verbs: the Vorfeld (preceeding a finite verb in second position), the Hauptfeld (between a finite verb in second position and infinitives or participles at the end) and the Nachfeld (anything following the last set of verbs). Consider this example:
Ich bin heute in die Stadt gegangen um einzukaufen.
The verbs responsible are bolded. The Vorfeld is occupied by ich, the Hauptfeld by heute in die Stadt and the Nachfeld by um einzukaufen.
Most German sentences will not have anything in the Nachfeld. However, almost all German sentence must include something in the Vorfeld. This is typically associated with the subject of a sentence or with something that requires emphasis. An empty Vorfeld will mark one of a very small class of phrases:
Imperatives; the verb must be first in these
Geh in die Stadt um einzukaufen!
Unmarked conditional clauses allow for a special construction:
Gehe ich in die Stadt, kaufe ich wahrscheinlich ein.
Which can be rewritten using a conditional subordinate clause in the following way:
Wenn ich in die Stadt gehe, kaufe ich wahrscheinlich ein.
(Note that the second main clause, kaufe ich wahrscheinlich ein has the first clause occupying its Vorfeld.)
Now sometimes, Germans don’t want to add emphasis to anything within a sencence and sometimes a sentence just naturally comes without a subject.[1] If that is the case and there is nothing to fill the Vorfeld, the sentence could be mistaken for a conditional clause. To prevent that, a syntactical expletive is added which merely fulfils the role of keeping the Vorfeld occupied in the absence of other candidates.
Es sind nicht alle gleich.
Es wird gefeiert.
(This second one is special, because aside from placing the past participle gefeiert into the Vorfeld there is nothing else that can go there; and ‘Gefeiert wird’ is not considered valid across all of Germany.)
In your case, the usage of the expletive is only due to reduce emphasis. There is nothing wrong with a sentence like:
Nicht alle sind gleich.
Gleich sind nicht alle.
Where the expletive disappears. Note that nicht alle is the sentence’s subject and hence the verb displays plural number.
A final note on your proposed alternative: the nicht is used to negate the alle in your example sentence. Thus, it must stay closely connected to alle. Putting them both into the Vorfeld is fine but separating them is not.
Alle sind nicht gleich.
The word order would be wrong. In this word order the sentence would mean that every single person is "not equal". However when speaking about single persons what does "equal" mean?
To say that it is not the case that all persons are equal the following word order is correct:
Nicht alle sind gleich.
User guidot posted a link about the word "es" in the following sentence:
Es regnet.
The situation here is different because in this case the word "es" cannot be left out while in the case of "Es sind nicht alle gleich" it is possible to write the sentence without the "es".
In the case of "Es regnet." or in English "It rains." you can see that the word "es" or "it" is used if a sentence does not give any information who is doing something but only about the fact that something is happening: Who is raining?
I don't know an official rule but my personal feeling as a native speaker is that the form using the "es" is used in some cases to express that the essential information is somehow different.
Example:
Drei Kinder sind heute zur Schule gegangen.
The information I would extract from this sentence is: What did the three kids do today? (Answer: They went to school.)
Es sind heute drei Kinder zur Schule gegangen.
The information I would extract from this sentence is: How many kids went to school today? (Answer: Three.)
Asking a teacher about the number of kids that came to school today he'll probably use the form using the "es".
Just like in the sentence "Es regnet." valid sentences seem never to contain (exact) information about who is doing something - at least in "modern" German language. You will typically never see sentences like:
Es gehe ich zur Schule.
Es gehst du zur Schule.
Es geht Max Müller zur Schule.
... in modern language. Sentences which are similar to the third example can sometimes be found in literature or old German.
