I would say, in the circumstances you describe, it would be a State Pension, corby. Many private pension schemes (mine included) extend benefits to widows/widowers in the event of the principle pension-holder dying. It is written into the terms of the scheme and the pension which has been funded by contributions into the scheme does not suddenly become a "benefit".
The government’s confusion between a pension and a benefit is perhaps understandable. State pensions are not funded from pensioners’ earlier contributions but instead, along with traditional benefits, are funded by current contributors. This, of course, is nothing more than a glorified Ponzi scheme, a practice that would see anybody in the real world up before the courts.
The DWP demonstrates a number of anomalies between their terminology and the real world as supported by English language. It pays pensions which it calls benefits and benefits which it terms pensions. It suggests that pensions are benefits because it suits their cause, but refuses to treat pensions as they do other benefits in terms of tax as State pensions, for people with other forms of income, form part of one‘s taxable income. Even the DWP itself suffers somewhat from an identity crisis because it deals predominantly with people who are not in work and suggests that it doesn’t pay pensions at all but age-related benefits! The fact that the government has legislated to make these changes official does not mean they are valid because, as far as I know, the government is not empowered to change the English language.
All this confusion has certainly worked its tricks on you. But you will probably find that most people who have contributed heftily to qualify for their fairly meagre State pension may not agree. They do not welcome it being lumped in with the same funds that are available to any work-shy layabout or anybody who has recently arrived on these shores upon their “retirement”.