Federal spending numbers at usgovernmentspending.com come from the OMB budget. They include direct spending on programs and also grants to states and local governments. State and local spending numbers come from the US Census Bureau. They are "direct spending" net of monies transferred to other governments.
Monies transferred to other governments are called intergovernmental transfers. To avoid double-counting at usgovernmentspending.com we show a “Gov. Xfer” column. It represents intergovernmental transfers from the federal government to the states and local governments. For instance, Medicaid (included under Health Care) is a joint federal-state program in which the federal government reimburses state governments for 50 percent or more of their expenses.
You can see that Health Care has the biggest “Gov. Xfer” number.
The intergovernmental transfer numbers used in the Numbers table are all Census Bureau “B” codes, as described in Census Bureau's Government Finance & Employment Classification Manual. For example, Census Bureau code “B01” is an intergovernmental transfer for “Air Transportation (Airports)”. The numbers are rolled up to provide the totals you can see at the top level.
If you drill down two levels (using the [+] controls) you will uncover the specific Census Bureau “B” spending codes used to compute the “rolled-up” intergovernmental transfer numbers. Each code is a link to the Census Bureau page that lists codes.
In summary, usgovernmentspending.com shows federal spending amounts as published by OMB that include monies transferred to other governments, but shows state and local spending as "direct spending" net of transfers to other governments as published by the US Census Bureau. Total spending is calculated as the sum of OMB federal spending plus Census Bureau state and local spending less "intergovernmental transfers" as published by the US Census Bureau.