I quote McWhorter, J. PhD Linguistics (Stanford), who explains the semantic nuance behind this distinction in two of his books.
Source: Our Magnificent Bastard Tongue (2009).
[p. 102 Bottom]
Learn a European language, including any Germanic language but Swedish, and note that quite often, while most verbs form their past perfect with the verb have—Ich habe gesprochen (“I have spoken”)—a good little bunch do it with the verb be, too—Ich bin gekommen (“I ‘am come’ ”). Just like in Old English: Learning had fallen away was “Learning was fallen away”: Lār āfeallen wæs.
Marking some verbs with be instead of have is a matter of being explicit about a certain nuance: in the perfect, the verbs marked with be refer, technically, to a state rather than an action; i.e., something that bes. When you say you have arrived, you mean that you have now achieved the state of being there: “I’m here, so let’s get started.” On the other hand, when you talk about how you raked leaves this afternoon, you usually are getting across that you per-
formed the action of raking leaves, not that you have achieved the state of having raked the leaves and are now ready to have your picture taken.
We English speakers think, “Well, yeah . . .” but hardly feel it necessary to split that hair. The other Germanic languages do split it—and Old English did.
But something strange started happening in Middle English, as usual; now it was the be-perfect that was falling away (like autumn leaves). By Shakespeare, be is used with only a few verbs
(“And didst thou not, when she was gone downstairs, desire me to be no more so familiarity with such poor people?” Henry IV, Part II, II, i, 96)
and today, it lingers on only in a frozen form such as The autumn leaves now are gone. Even there, you may well have thought of gone as an adjective (The leaves are red, The leaves are gone), and in any case you can also say The autumn leaves have gone, which, in this case of the grand old Old English be-perfect, they have, as always in English.
Source: What Language Is (2011), p. 27 Top.
Or, what part of speech is gone in She is gone? Call it an
adjective—and explain why you can't say a gone dog as you can
say a brown dog. She is gone is English's wan gesture toward
something robust in its Germanic relatives, in which a whole
group of verbs take be instead of have in the past, because they
describe something that is more how you are than what you
did. To be gone is just that, to be gone. Sure, it is also technically
to "have" exerted the action of leaving, but we think more read-ily of the result of the leaving, that one is in the state of being
gone. Thus just as French has Il est allé, "He is gone," German
has Er ist gegangen. All of the other Germanic languages have
the equivalent, or almost all (what's up with you, Swedish?).
English crudely forces have on every verb, and while Swedish
does, too, that's just one coarseness, as if it happened not to
learn to put a napkin in its lap but still went about in double-
breasted suits and cultivated orchids. English, in comparison,
just-the-facts-ma'am across the board, is Cro-Magnon.