Is re-using parts of one's own SoP (or research statement) considered self-plagiarism? Are the following considered instances of self-plagiarism?


Re-using parts of one's own statement of purpose (submitted as part of a graduate admission application) in SoPs submitted with other graduate admission applications, during same/different admission cycles
Re-using parts of one's own research statement in SoP(s) or vice-versa
It is very unlikely that anyone would consider either of these problematic. An SoP isn't published formally, for example. 

People reuse their own words in other contexts all the time. But self plagiarism arises when you publish something that is based on or contains elements of something that you published previously without citing the original.

The reason that this is a problem is that a person reading the new work wants to know the complete context in which it was developed. This is why you cite other works. But it is also why you cite yourself, rather than just reusing your words. 

The original publication, itself has a context, not only what it says, but the references it cites. If your new publication doesn't point to that, the reader will find it hard to know the complete context. Scholarship builds on earlier scholarship. Lack of citation cuts the chain of context that is essential for the complete picture. 

But the two cases you point to don't require the same chain of evidence to be maintained, so there is no issue.