I think that you may be confusing taxes?
The VAT on leased cars is recoverable by VAT registered businesses on their VAT return, in the same way that they recover the VAT incurred on their other business expenditure. The only difference is that recovery is restricted to 50% of the VAT charged, this is because of the possibility that the car may also be put to private use. Any business that is not VAT registered is unable to recover any of the VAT incurred on their business expenditure. More detail regarding the VAT treatment of cars is here: https://www.gov.uk/guidance/vat-on-motoring-expenses-notice-70064
You haven’t provided a link to this “Claim Tax Relief Expenses Wizard”, but that type of wording normally applies to income or corporation tax, on salaries or business’ profits – not VAT. For example, if this is the page that you’re looking at https://www.gov.uk/tax-relief-for-employees, it calculates what income tax relief an employee might be entitled to if they incur certain types of expenses as part of their employment, which aren’t reimbursed by their employer.