How the three methods differ
Salary sacrifice reduces gross pay before tax and employee NI are calculated.
Net pay usually reduces taxable pay for income tax but not employee NI-able pay.
Relief at source is usually deducted after tax, with basic-rate relief added by the pension provider.
Why take-home pay can change
If a contribution lowers taxable pay, income tax can fall. If it lowers NI-able pay, employee NI can also fall.
Relief at source may show a smaller payroll deduction than the gross pension contribution because the provider claims basic-rate relief. Higher-rate or additional-rate relief can depend on separate claims and is not fully modelled here.
This is not advice
The best pension arrangement depends on employer scheme rules and personal circumstances.
This site explains calculation mechanics only. It does not recommend a pension scheme or financial decision.