There are three big differences, in addition to many similarities. The first big difference – which is HUGE in terms of importance – is that this pension is 100% in your own name. This means that unlike a company pension plan where all the pension assets, of all the employees, are lumped together into one account, your pension assets are entirely separate. This prevents any chance of you being worse off due to other people’s actions (or inactions).
The second big difference – also HUGE in terms of importance – is that because it is 100% in your own name, nobody can change the terms and conditions and leave you worse off. This happens with alarming regularity in both corporate and government pensions. Company directors have the authority to change the terms and conditions of a company pension scheme – sometimes even to the extent of changing what you get at the end – and governments often change state pensions when it is politically convenient to do so, which can include extending the duration (making you work longer before you can receive pension payouts), and cutting the amount you receive. When this happens – and it has happened lots, notably in Greece but also many countries elsewhere – it is usually discussed and agreed in private, then simply announced and enforced immediately. There are many examples of this, just research it online – here’s one to get you started: https://www.bbc.com/news/world-europe-19298681
The third, smaller but certainly important difference is in how your pension is invested – which affects how much it will be worth in future. Corporate pension plans have a board of trustees, who decide (or appoint someone to decide) what the group pension plan invests its money into. Whilst you might think that this isn’t a big issue, it’s a huge issue when they make bad decisions, because it means that as a result of someone else’s decision – someone whose (relatively high) salary is being paid for from your pension assets – you get less money in future. Again there are lots of examples of this, do some research online – here’s one to get you started: https://www.pasadenastarnews.com/2020/08/05/pasadena-state-pensions-investment-strategies-threaten-citys-finances/. By comparison, this pension plan is 100% invested into the S&P500 Index and does not have politically or corporately appointed decision makers who can decide to invest it into something else instead.
If you’re still not convinced, know that in general, there is a huge gap between the value of pension assets – both public and private – and the amount they owe in future. This “funding gap” is not pretty, and financial experts expect it to be a total disaster at some point in the relatively near future. Have a look at this, it’s only a two-minute read but very effectively illustrates the problem: https://ig.ft.com/sites/pensions-interestrates-explainer/
Get a pension plan in your own name. Future You will thank you for it.