"O descendants of Abraham his servant, O sons of Jacob, his chosen
ones. He is the LORD our God; his judgments are in all the earth. He
remembers his covenant forever, the word he commanded, for a thousand
generations, the covenant he made with Abraham, the oath he swore to
Isaac. He confirmed it to Jacob as a decree, to Israel as an everlasting
covenant" Psalm 105:6-10
Israel was indeed called God’s elect or "chosen ones". The term is
used in many New Testament writings too. However the context that it was
used in demonstrates that it applies to the assembly of called out ones
or "the church", the Body of Christ. This is one such section of verses
that demonstrates this principle.
"For whom he did foreknow, he also did predestinate to be conformed
to the image of his Son, that he might be the firstborn among many
brethren. Moreover whom he did predestinate, them he also called: and
whom he called, them he also justified: and whom he justified, them he
also glorified. What shall we then say to these things? If God be for
us, who can be against us? He that spared not his own Son, but delivered
him up for us all, how shall he not with him also freely give us all
things? Who shall lay any thing to the charge of God's elect? It
is God that justifieth. Who is he that condemneth? It is Christ that
died, yea rather, that is risen again, who is even at the right hand of
God, who also maketh intercession for us. Who shall separate us from the
love of Christ? shall tribulation, or distress, or persecution, or
famine, or nakedness, or peril, or sword? As it is written, For thy sake
we are killed all the day long; we are accounted as sheep for the
slaughter. Nay, in all these things we are more than conquerors through
him that loved us. Romans 8:29-37
To the Hebrews the following comment was made: "But you have come
to Mount Zion, to the heavenly Jerusalem, the city of the living God.
You have come to thousands upon thousands of angels in joyful assembly,
to the church of the firstborn, whose names are written in heaven. You
have come to God, the judge of all men, to the spirits of righteous men
made perfect, to Jesus the mediator of a new covenant, and to the
sprinkled blood that speaks a better word than the blood of Abel."
Hebrews 12:22-24
Why are these terms used and why is Israel confused with or
intermixed with elect, assembly etc?
The real misunderstanding is because people don’t know or forget what
the term Israel means. To truly understand this name you need to go back
to when the term was given out. "Then the man said, "Let me go, for
it is daybreak." But Jacob replied, "I will not let you go unless you
bless me." The man asked him, "What is your name?" "Jacob," he answered.
Then the man said, "Your name will no longer be Jacob, but Israel,
because you have struggled with God and with men and have overcome."
Genesis 32:26-28
From the context of this passage you would think the term means
overcomer which is indeed close but the actual meaning of the name
Israel is "prince of God" or "son of God". When you keep that
meaning in mind you now can see what is meant by the term and how it is
used in so many places of the Bible. This does not mean that in some
locations it is not used to describe Israel as a nation but that it is
the meaning of the term to God.
It is also easier to understand why the term is used to directly
refer to Jesus the Son of God.