The Senate on Tuesday evening voted on party lines to adopt a budget outline designed to clear the way for a major piece of President Trump’s domestic agenda, putting forth a measure that calls for increasing spending on immigration enforcement and defense while cutting other federal programs.

Republicans in Congress have been consumed for weeks with advancing a budget blueprint to power their push to enact Mr. Trump’s sweeping tax and immigration agenda. Approval of such a plan is a crucial first step if Republicans want to avail themselves of a process called budget reconciliation, which allows legislation that affects government revenues to pass the Senate on a simple majority vote.

For decades, both parties have used that maneuver to push major domestic policy legislation through Congress — including tax cuts, health care policy changes and economic relief packages — over the opposition of the minority party. The stakes are exceedingly high, and the process is tremendously difficult.

The House and Senate, both controlled by Republicans, have been working on separate budget plans and are at odds on how to move forward. With the House G.O.P. divided and delayed in considering their outline, the Senate is moving ahead.

Here’s what you need to know about the budget.

What is a budget resolution?

In theory, Congress is supposed to adopt a budget resolution each year setting a top-line number for federal funding and providing general contours for how that money should be spent. After the plan is approved, it falls to lawmakers on the Appropriations Committees to allocate federal dollars, following the blueprint.

Lawmakers in recent years have not produced such a plan or put it to a vote, sidestepping tough decisions about what programs to spend on and what programs to cut. Instead, congressional leaders, in collaboration with senior appropriators, have agreed on the overall numbers and simply passed spending legislation each year.

But in order to use the reconciliation process, the House and the Senate must each adopt a budget resolution that lays out broad areas of agreement on where to increase and decrease spending.

The budget resolution is just a blueprint. Unlike a spending bill, it does not carry the force of law, and it does not fund the government. Its consideration is entirely separate from another task that Republicans in Congress have in the weeks ahead: agreeing to and passing legislation to keep federal funding flowing past a March 14 deadline.

The budget measure being considered this week does not even lay out what specific legislative changes to take in order to meet the spending targets it contains. Those changes must be detailed in separate legislation — one or multiple bills — that is subject to restrictive rules for what can be included and which must pass both the House and Senate to become law.

What’s the difference between the House and Senate blueprints?

The Senate blueprint is far more bare-bones than the House plan. It calls for increasing military spending by $150 billion. Funding for border security measures, including additional detention beds and Immigration and Customs Enforcement agents, would increase by $175 billion. It does not lay out specific spending cuts to pay for those increases, but Senator Lindsey Graham, the South Carolina Republican who chairs the Budget Committee, has indicated that the legislation would be fully paid for, in part through new revenues from domestic drilling.

Mr. Graham has said the blueprint represents just the opening salvo in the Senate’s legislative drive, and that it would be followed by a second bill that would extend the 2017 tax cuts.

The House plan is both more expansive and more granular, in an effort to meet the demands of conservative hard-liners who have demanded that House G.O.P. leaders guarantee deep spending cuts.

That blueprint calls for legislation that would add roughly $3 trillion to the deficit over a decade, while imposing deep cuts in spending on health care and food programs for low-income people. That would help pay for $4.5 trillion in tax cuts. It also calls for raising the debt limit by $4 trillion.

Why are the House and the Senate advancing different plans?

House and Senate leaders have remained divided over the best way to enact Mr. Trump’s fiscal promises into law. In the Senate, Republicans have argued that lawmakers should deliver the president an early political victory and quickly pass legislation increasing funding for immigration enforcement, arguing that the Homeland Security Department desperately needs more money to carry out the White House’s ambitious deportation agenda.

But G.O.P. leaders in the House have argued that lumping Mr. Trump’s entire domestic policy agenda into one big bill will make it easier to pass in a chamber where Republicans have a razor-thin majority and will need to muster near-unanimity in order to pass the blueprint.

Senate leaders initially deferred to the House, but after internal divisions slowed their efforts to put together a budget plan, Mr. Graham went ahead and advanced his own plan.

What programs are on the chopping block?

Because the budget resolution only lays out broad spending targets by committee, Republicans have not yet had to choose which federal programs they will cut — or by how much.

But the House blueprint hints at where Republicans plan to find the money to finance their tax cuts. For example, the plan instructs the Energy and Commerce Committee, which oversees Medicaid, to come up with at least $880 billion in cuts. That accounts for more than half of the reductions laid out in the budget outline.

Those choices will be among the toughest Republican leaders will have to make, especially in the House. They will need to balance the demands of hard-right conservatives who want to gut Medicaid and food stamps against the entreaties of politically vulnerable moderates whose constituents rely on those programs.

At the same time, they will have to decide which tax cuts championed by Mr. Trump are essential, and which they can jettison. Just extending the 2017 tax cuts alone would cost roughly $4 trillion over the next 10 years.

Andrew Duehren contributed reporting.