There's still a difference, and you'll understand it if you dig deeper in study of God's Word. Bible prophecy which God gave through His prophets to Judah (house of Judah) is one thing, and prophecy given to Israel (ten tribe house of Israel) is another. After God split old Israel into the two houses, this prophetic distinction is made for each house a lot. One need only pay attention, because after the split the Jews are distinguished as Judah, Jerusalem, kingdom of Judah, or house of Judah. But the ten tribes of Israel are distinguished as Israel, kingdom of Israel, Samaria, Ephraim, or house of Israel.
Also, God removed the ten tribe house of Israel from the land, scattering them to Assyria and the land of the Medes, about 120 years prior to Judah's seventy years captivity to Babylon. The ten tribes never returned to the holy land, but a small remnant of the Jews did return from their Babylon captivity (Ezra 2). The rest of the house of Judah chose to say in Babylon after the 70 years, because God kept His promise to take care of them there. Then from there they were scattered through the countries like Israel was. The Jews kept their heritage as part of Israel though, as God promised they would in Hosea. But the ten tribes of Israel lost theirs, living as Gentiles among Gentiles, which also God said He would cause them to do.
If you believe that then you really don't understand about God's promise to David.
Josephus said the term Jew actually began with the small remnant of the house of Judah that returned to Jerusalem from the Babylon captivity. But really, the distinction was more likely prior to that, once God split old Israel into two separate kingdoms. Those of the southern kingdom of Judah would then have likely began making the distinction between Judah and the northern house of Israel (ten tribes).
The reason why the title of Jew came to represent Israel only is because God scattered the ten tribes making them lose their heritage as Israel, as per His warnings of rebellion against Him per Deut.4 & 28. But it doesn't mean the Jews are the only people of Israel though. Lot of today's Jews like to play out the Count of Monte Christo theme against the ten tribes, acting like they no longer exist, but that doesn't work with our Heavenly Father, for He knows where He scattered the ten tribes which make up the majority of the peoples of His Israel, which is what the Amos 9:9 Scripture is about.
Scofield's reputation is what 'he' made it, not others using hate speech against him. He didn't create the Dispensationalist doctrine you speak of anyway. He only got monies from New York bankers to put Darby's theories in print, so as to deceive peoples, and of course to make a lot of money, his main aim no doubt.