Although israel is accepted as a state by some western countries, it did not exist before 1948, neither did israelis, prior to 1948 they were called Palestinians.
Isaelites are not israelis; israelites were not jews either.
When Persia conquered and designated the area as jehud, they eventually allowed israelites that were in exile to return, these israelites then became jehudites.
This is where the word
jew comes from and not before the end of the 6th century, even still it's a technical term having to do with living in jehud; the word
jew doesn't become an ethnic term for quite some
time.
Ashkenazi (Indo-European) jews are not Semites and have no genetic link to the land of Palestine. The ashkenazi converted to judaism after Arab jews migrated north into
Europe.
In the largest genomic
study of ashkenazi jews, their origins trace back to four primeval villages in north-east Turkey. The ashkenazi jews began relocating from ancient Ashkenaz to the Khazar Empire to expand their mercantile operations and the demise of Khazaria led to the ashkenazi splitting into
two groups – some remaining in the Caucasus and others migrating into eastern
Europe and
Germany.
The
two groups still called themselves ashkenazi, however the name became more strongly associated with
Germany and the European group, for whom yiddish became their primary language.
The original
jews were Arabs (Semites) from the area now known as israel, a.k.a. Occupied Palestine.
Only those that practice judaism are jews. Once you change your religion or become an
atheist, you are no longer a
jew.