The Democrat CR would NOT end the shutdown.

IF the Republican CR passed the Senate today, the President could sign the bill and the government would immediately re-open, right? HOWEVER, the Democrat 'CR' has NOT been passed by the House of Representatives. THEREFORE, even if passed by the Senate, the Democrat bill would need to go BACK to the HOUSE, to be voted on by them, mostly Republicans. This would go right back to major budget negotiations and the government would stay shut down. So Schumer and the Democrats are lying (surprise) when they say that the Republicans in the Senate can solve this immediately. Am I right?