Are "перекрестье" and "перекрестие" two different words with different meanings? Or are they two variants of the same word? Can they be used interchangeably?
перекре́стие, -я (в оптике)
Refers to optics, such as cross hairs in a gun optical scope
перекре́стье, -я, р. мн. -тий
Refers to an intersection of something or something that forms a cross.
Words ending with '-ие' such
создвездие and so on quite often have alternative form ending with
-ье, like in
-ье form is either poetic, obsolete and/or used in colloquial speech.
The answer provided is strictly speaking wrong. Let's refer to the link provided:
перекре́стье ср. разг. Место пересечения чего-л. То, что имеет форму креста.
So, this is just a colloquial form.
The other thing is that for some words there's indeed a tendency to designate different things - like
воскресенье for Sunday and
воскресение for the Resurrection.
May be we are facing the same kind of process with
перекрестие but I'd rather say they these words are interchangeable but
перекрестие is preferable.
They have exactly the same meaning. In written Russian, nouns ending in '-вие', '-тие' or '-лие' are often changed to use '-ье' instead for a poetic, sublime, or 'old-fashioned' effect: призванье, долголетье, страданье, тренье, понятье, бесправье. - however, you won't encounter those in nowadays speech very often.
A reverse substitution can sometimes be observed in some nouns ending in '-ье': похмелие, веселие, бездорожие, although one will typically find such usage only in pre-20th-century written sources or in texts mimicking those.