So you are saying there’s no difference legally between an OMNIBUS bill vs a budget bill? Then where are folks coming up with the purported big difference from? What about the purported record of OBummer ignoring all the OMNIBUS bills for his 8 years and doing what he jolly well wanted with the money thereby provided?
That is quite a bit to unwrap.
First, "Budget Bill" is sloppy usage, like "Russia investigation" is sloppy usage. There is a world of difference between a budget and an appropriation.
What was signed into law yesterday was a spending or appropriations bill. There are supposed to be 12 separate spending/appropriations bills. When hey get rolled into one, the spending bill is referred to as an omnibus bill, but it is still a spending/appropriations bill. It is akin to writing the check, which is different from budgeting in advance of writing the check.
Congress hasn't followed the process since 1997.
On the subject of budgets, Congress passes Budget resolutions, but these are not signed into law. The budget resolutions guide the drafting of appropriations.
On the subject of Obama ignoring appropriations, all presidents do to some degree. At an extreme degree, the president would purport to "impound" all of some appropriation, say for example the line that deals with Planned Parenthood.
Back to your questions. The differences between an omnibus appropriations bill and a budget bill are several. One of them is that a budget bill does not allocate funds, another is that a budget bill is never signed into law, and another one is that an omnibus appropriation is a collection of what would usually be 12 separate laws.
Whether omnibus or 12 separate laws (or some combination in between, say 6 committee bills and one bill to cover the other 6 committees), appropriations are ALL THE SAME. There is NO difference between an appropriation made as part of a single committee appropriation, versus the same appropriation made in an omnibus appropriations bill.
As for where people get their cockamamie ideas, I don't know, I don't care, and the ignorance is on them, not on me.
As for the purported record of Obama ignoring all the OMNIBUS bills for his 8 years and doing what he jolly well wanted with the money thereby provided - as a blanket proposition, it is BS. I'll bet at least 80% of the appropriated funds were spent exactly as appropriated. That can't happen if he ignores the appropriations laws.