As this article in the Spanish Wikipedia notes:
El vocablo «Filipinas» deriva del nombre del rey Felipe II de España.
The Philippines were named for King Philip II of Spain. They were «Las Islas Filipinas», which was anglicized to the Philippine Islands.
The noun form retains the F (Filipino), while the adjective form uses Ph (Philippine Embassy).
(I've seen older texts in British English that referred to the natives as "Philippinos.")
As to why, there's this answer:
English never had a suitable equivalent for Filipino – a “Philippine,”
“Philippian” or “Philippinian” probably just didn’t sound right, so
English adopted the Spanish word Filipino, retaining the letter F and
the suffix, “ino."
It's interesting to note that the country's official appellation in Pilipino is Repúblika ng Pilipinas. The Pilipino Express article explains that as well.
Edit: Slate has another take on Filipino/Philippines, but still doesn't explain the discrepancy in spelling between the noun and adjective forms.
Since your's and her's are virtually always incorrect in modern English, one way to answer your question is to look at the frequency of those terms in published books.
Searching Google Ngram Viewer for your's and her's shows the terms peaking in popularity around Jane Austen's lifetime and virtually extinct by 1850.
Best Answer
While English spelling became more and more standardized after the printing press was introduced in 1475, it was not considered important until the 19th century. In the U.S., universal standardization was spurred by Noah Webster's ideologically motivated 1783 speller and 1828 dictionary, and by Horace Mann's efforts and the start of universal public schooling in various states from the 1830s onwards. The dictionaries did not include proper nouns, so names were among the last words to get standardized spellings, as any exasperated genealogist sifting through old passenger manifests and Census data knows.
Probably a dozen forms were in use in the late 1700s. Both Pensylvania and Pennsylvania appear on the original U.S. Constitution, notable as not only was the document composed in Pennsylvania, but the secretary, one Jacob Shallus, was a scribe for the Pennsylvania state legislature and presumably one who ought to know.
Multiple spellings frequently appear in the same document, sometimes just a few words apart:
… or no words apart:
Indeed, Seymour Stanton Block's 2004 biography of the commonwealth's most famous son, entitled Benjamin Franklin, Genius of Kites, Flights and Voting Rights, reports that as an anti-counterfeiting measure,