What is the difference between Jews and Hebrew?

Answer 1

None. Same people, different eras.

"Hebrews" (Ivrim) actually means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back.
In 1934-39, excavations were conducted at ancient Mari on the Euphrates River. They found that ancient towns were named after the ancestors of Abraham: The city of Nahor was found near the city of Harran which exists to this day. Equally clear signs of early Hebrew residence appear in the names of other towns nearby: Serug (Assyrian Sarugi), Terah (Til Turakhi, "Mound of Terah"), and Peleg (Paliga, on the Euphrates). All these names are found in Genesis ch.11.
Abraham himself was called a Hebrew (Genesis 14) because of his ancestors, not because he was the first one. That is the simple meaning of Genesis 14:13. Poetically, however, Abraham is called Ivri because the name also translates to "other side." Abraham was on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings spread.
In that sense, "Hebrews" is often used to refer to Abraham's Israelite descendants. Thus it refers to the Jewish people.
"Israelites" refers to the people down to about the time of the destruction of the First Temple some 2500 years ago. "Jews" refers to the people from Second Temple times onward, because after the Assyrian conquest the remaining Israelites were (and are) mostly from the Israelite tribe of Judah.

Answer 2

Nothing, except that in modern usage, the word Jew refers to the person, and Hebrew refers to the language.

Another answer

Same people, different eras. "Hebrews" (Ivrim) actually means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back.
In 1934-39, excavations were conducted at ancient Mari on the Euphrates River. They found that ancient towns were named after the ancestors of Abraham: The city of Nahor was found near the city of Harran which exists to this day. Equally clear signs of early Hebrew residence appear in the names of other towns nearby: Serug (Assyrian Sarugi), Terah (Til Turakhi, "Mound of Terah"), and Peleg (Paliga, on the Euphrates). All these names are found in Genesis ch.11.
Abraham himself was called a Hebrew (Genesis 14) because of his ancestors, not because he was the first one. That is the simple meaning of Genesis 14:13. Poetically, however, Abraham is called Ivri because the name also translates to "other side." Abraham was on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings spread.
In that sense, "Hebrews" is often used to refer to Abraham's Israelite descendants. Thus it refers to the Jewish people.
"Israelites" refers to the people down to about the time of the destruction of the First Temple some 2500 years ago. "Jews" refers to the people from Second Temple times onward, because after the Assyrian conquest the remaining Israelites were (and are) mostly from the Israelite tribe of Judah.
In 2000, the analysis of a report by Nicholas Wade "provided genetic witness that Jewish communities have, to a remarkable extent, retained their biological identity separate from their host populations, showing relatively little intermarriage or conversion into Judaism over the centuries. The results accord with Jewish history and tradition and refute theories which would allege that Jewish communities consist mostly of converts."

Answer 3

"Hebrews" (Ivrim) means descendants of Eber (Ever). Ever was an ancestor of Abraham (Genesis ch.10-11) and the earliest Hebrews were Abraham's uncles and cousins for several generations back. They were among the Western Semites and lived in northern Mesopotamia, near the confluence of the Balikh and the Euphrates.
Abraham (18th century BCE) was called a Hebrew (Genesis ch.14) because of his wider family.

Poetically, however, Abraham himself is called Hebrew because that name (Ivri) also translates to "the other side." Abraham was figuratively on "the other side" since he was the only monotheist (Midrash Rabbah 42:8) until his teachings took root. His ancestors and cousins had slipped into idolatry well before his time, as is evident from Genesis 31:30, 31:53, and Joshua 24:2. For that reason, Jews do not bestow on them the honorific title of ancestors despite the genealogical connection.
We credit Abraham as our first ancestor despite knowing exactly who came before, since it was Abraham who founded our beliefs. Thus, "Hebrews" is often used to mean Abraham and his Israelite descendants, instead of his wider family. In this sense it can refer to the Jewish people.

• Link: Abraham's biography
  

The word "Hebrews" can continue to refer to Abraham's descendants until the lifetime of Jacob. After that, we prefer "Israelites," since Jacob was given that name by God (Genesis ch.35), and it is considered a national title; one of honor. "Israelites" refers to the people (Jacob's descendants) down to the Assyrian conquest (133 years before the destruction of the First Temple), some 2600 years ago.

• Link: Jewish ancestry
  

"Jews" refers to the same people, from the end of First Temple times up to this day, because after the Assyrian conquest the Israelites who remained in the land were (and are) mostly from the Israelite tribe of Judah, and the land was then called Judea. But all the above terms are occasionally interchanged.

In modern usage, we prefer to use the term "Hebrew" only to refer to the language.

Answer 4

A Jewish person is a Jew.

Hebrew is a language.