More can be said, but /u/amazonstar gave an excellent response a few months ago to a similar question.

To add to my previous answer on omnibus appropriations bills that /u/robbyslaughter posted (thanks!)...

With regard to policymaking through spending bills, both the House and Senate have explicit provisions in their rules prohibiting program authorizations in appropriations bills. The 12 annual appropriations bills - several of which are frequently combined into an omnibus spending bill - cannot be used to change the law or fund programs that are not already authorized by law (with a few limited exceptions).

These are long-standing rules that date to the mid-1800s and were established precisely because legislators were trying to attach unrelated and often controversial provisions to spending bills. In 1835, Congress failed to pass a fortifications bill (a sort of precursor to what we call Defense appropriations today) because the House included a provision giving President Jackson a $3 million blank check to spend on military operations and the Senate objected. The bill died and John Quincy Adams - who was then a member of the House - proposed a rule that appropriations bills should not include anything besides appropriations for authorized programs so they would pass more easily. After two years of struggling to pass the fortifications bill, they established the rule in 1837.

The 1837 rule was was generally interpreted to also prohibit legislating in appropriations bills, but that language was added in the 1880s after the "1879 Rider Wars." Democrats attached riders to multiple appropriations bills to repeal elements of the Enforcement Acts, specifically provisions stationing troops and federal marshals at southern polling places for election supervision. Their assumption was that President Hayes would not veto the bills because they were needed to fund the government, but he called their bluff. Eventually the bills were passed without most of the election riders, but it was a 14 month fight that wasn't fully resolved until the end of the session, with two weeks left in the fiscal year they were trying to fund. This leads to the rule explicitly prohibiting "any provision changing existing law" in an appropriations bill, which is still adhered to today.

As a result, while the annual spending bills are frequently combined into omnibus spending bills, they are (mostly) limited to the allocation of money to existing federal programs. (Two notable exceptions to this rule are continuing and supplemental appropriations, which are not considered general appropriations bill and therefore not subject to rule XXI (House) or Rule XVI (Senate), but these are generally not used for major policy changes or program creation as they are carefully crafted to ensure passage in response to an emergency or an impending government shutdown).

Where you do observe programmatic policy changes in budgetary bills is the budget reconciliation process. The budget reconciliation process was established in the Congressional Budget Act (CBA) of 1974, which was intended to shift control over the federal budget process from the president back to the Congress. President Nixon campaigned on limiting federal spending in 1972 and although he vetoed nine of the FY 1973 appropriations bills, his vetoes were overridden, which led him to just not spend the money Congress had appropriated, under a process called impoundment. This leads Congress to pass the Congressional Budget Act, which established the House and Senate Budget Committees and the Congressional Budget Office as well as creating a streamlined congressional budget process and mostly eliminating impoundments.

Under this new, streamlined budget process, the House and Senate are supposed to agree on a budget resolution each year that sets top-level spending and revenue levels for the upcoming fiscal year. Those levels are then used by the Appropriations Committees as they craft the annual spending bills. This annual budget resolution may include "reconciliation instructions" that direct various committees to meet spending, revenue, and/or deficit targets. The primary intention of this process was to allow Congress to ensure current law matches up with the budget resolution. If the budget committee sets targets for the upcoming year based on the assumption that Congress will do X, they want to ensure X - or the equivalent fiscal change - happens. So the instructed committees draft legislation to alter spending and/or revenue as needed and the resulting bill is fast-tracked through Congress. Most importantly, it can't be filibustered in the Senate because budget resolutions are considered privileged under Senate rules.

The first use of the reconciliation process was in 1980 with the Omnibus Reconciliation Act of 1980, which was intended to reduce the FY81 deficit by about $8 billion. The resulting bill is 97 pages long and covers a wide assortment of changes to federal programs from cuts to child nutrition subsidies to establishing a 20% capital gains tax on nonresident aliens, but these are all relatively minor adjustments relative to the size of the federal budget. The next year, Reagan uses this process to fulfill his campaign promise of cutting non-defense spending across the board. Although the purpose is again deficit reduction, it should be noted that this is accomplished primarily through policy changes. The bill doesn't simply reduce appropriated funds, it changes the underlying laws to do things like eliminating the minimum Social Security benefit and establishing various block grant programs. The Omnibus Budget Reconciliation Act of 1981 had the votes to ass the Senate even if it had been filibustered, but the reconciliation process was used because it allowed changes to be made to programs across the government in one go, rather than passing a social security bill, and a head start bill, and a welfare bill, etc.

Budget reconciliation was used eighteen times between 1980 and 2001 and while some years were minor budgetary adjustments, others have been pretty significant policy changes from establishing COBRA coverage to expanding the Earned Income Tax Credit and establishing new income tax brackets. Of the pre-20 year rule reconciliation bills, the most well-known instances are probably welfare reform in 1996 and the first Bush tax cuts in 2001. In both instances, the reconciliation process was thought to be necessary to overcome a filibuster in the Senate (although in the case of welfare reform it ended up being unnecessary). All of the reconciliation bills have bundled together changes to an assortment of federal programs to some degree. Since 1985, reconciliation bills are limited to provisions that would have more than a non-incidental effect on federal spending or revenues, but that's a pretty broad limit.

There are also instances of multiple authorization bills combined into one, or one bill being included as a rider on another and those are sometimes called omnibus bills, but that's been going on forever to forge voting coalitions and separate from spending/budgetary bills.