I think too often that any government program gets lumped into welfare. That may play into current political debate but it doesn't really match the definition. Here's what Merriam Webster online says:
The key is the connection to an individual in need. Employment by the government is not welfare since it is money in exchange for work. Government services available to the public at large would not be welfare either.
In higher ed an academic scholarship to a state university would not count, but a need-based scholarship would count.
Tax policy is designed to favor or disfavor certain types of economic activity, and are not really about money for those in need. An exception would be the earned income tax credit or disability-based exemptions which could meet the definition.