The two constructs ‘etc.\@ ’ and ‘etc.\ ’ have the same ultimate effect, of not ending a sentence after a period (following a lowercase letter). You may well wonder when to use which one.
The answer is, in normal use, it does not matter, because the result
is identical, even though the two commands do quite different things.
The first assigns 1000 to \spacefactor and any effect will
depend on the following characters; the second inserts an explicit
glue item into the output. But in the end, normally, the standard
interword glue is inserted either way. It is more common and perhaps
intuitively simpler to use ‘\ ’.
The above are ways to avoid getting end-of-sentence spacing in the
wrong place. On the other hand, sometimes you need to end a sentence
in a context LaTeX doesn’t recognize. The most common is after a
capital letter which, as we’ve already seen, can also be handled with
\@ (see \@). But \@ does not always suffice.
One example is when a sentence ends with an ellipsis (\ldots):
This long idea \ldots\ Another idea ...
Here, we want end-of-sentence spacing after the ellipsis, since the subsequent text is starting a new sentence.
Another example is when the purportedly sentence-ending punctuation is before a reference:
... some quoted text.''\ [20]
Here, it is the reference [20] that is the end of the sentence in the document, not the period that ends the quotation; hence the backslash-space after that period and the closing quotes. It is conventional not to use two periods in this case.
The only way we know of to forcibly insert end-of-sentence spacing in
such unusual circumstances is by setting \spacefactor
explicitly to 3000. Here is a macro that does it:
\newcommand\sentencespace{\spacefactor=3000{}\space\ignorespaces}
The empty braces tell TeX that the integer value is complete; the
\space inserts a normal space, just as if it had been typed;
the \ignorespaces ignores any extra spaces that might follow in
the input. (These commands all come from TeX, not LaTeX.) The
first example can then become:
This long idea \ldots\sentencespace Another idea ...