You are correct. The term election aka chosen does have different flavors of application. One application IS meant primarily as election to service for Israel. Not so in the new testament when it is applied to Christians. The term election has a far different aspect to it, a far different application.
May I point out that the term election in Strongs 1586 and 1589 carry with them the quality of foreordination and predestination. Indisputably.
https://biblehub.com/greek/1586.htm
https://biblehub.com/greek/1589.htm
1586 eklégomai (from 1537 /ek, "out of" and 3004 /légō, "speaking to a conclusion") – properly, to select (choose) out of, by a highly deliberate choice (i.e. real heart-preference) with a definite outcome (as with the destination of divine selection for salvation).
Cognate: 1589 eklogḗ (from 1537 /ek, "out from and to" and3004 /légō, "speaking to a conclusion") – properly, selection out of and to a given outcome; (theologically) election. See 1586 (eklegomai).
May I point out that the term election in Strongs 1586 and 1589 carry with them the quality of foreordination and predestination. Indisputably.
https://biblehub.com/greek/1586.htm
https://biblehub.com/greek/1589.htm
1586 eklégomai (from 1537 /ek, "out of" and 3004 /légō, "speaking to a conclusion") – properly, to select (choose) out of, by a highly deliberate choice (i.e. real heart-preference) with a definite outcome (as with the destination of divine selection for salvation).
Cognate: 1589 eklogḗ (from 1537 /ek, "out from and to" and3004 /légō, "speaking to a conclusion") – properly, selection out of and to a given outcome; (theologically) election. See 1586 (eklegomai).
It's about the same as the NIV translating "sarx" into "sinful nature," human beings realizing their theology is not express enough so altering Biblical terms to suit their theological conclusions.