The holy calling is according to God’s purpose. His purpose was given to us before the times of the ages. Both the Second Timothy and the Ephesians verses should be understood be two important elements. There is an election to something; what is being elected? Who are persons being elected? Who are the “us in Christ?”
There is nothing inherent in the meaning of the verb “to choose” that implies salvation. The common use of electing or choosing people for public office is a good English equivalent of the Greek verb. Many people are elected or chosen to office all the time. The verb is very generic.
The word to choose in Greek “ἐκλέγομαι” occurs 19 times in the New Testament. Only perhaps three or four times does this verb mean an election to salvation. Thayer’s Greek-English Lexicon of the New Testament, an early scholarly work in English has been a basic reference book since 1885. In this book he lists at least five different types of election relating to this verb: