This is how US politics work. The current president makes a proposal on how they would like for the budget to look, but it's just a proposal. The legislative branch (Congress) is actually responsible for creating the budget. They are not at all obligated to follow the proposal.

The president has to agree to the budget submitted to him by Congress, so there's usually a lot of discussions between the two parties. The caveat here is that Congress can override a presidential veto.

The administration (ie. the Trump administration, ie. the executive branch) has no control over spending and the president's budget is more of a wishlist than anything else. Congress sets the budget and passes the bill(s) that fund it.

This is the budget that Trump threatened to veto and whined and complained about before he signed, and the one they're writing articles about the Democrats getting heaps of stuff they wanted in it. I don't think it should be taken as an indication of stuff Trump wants, and to some extent the same goes for the GOP.