Most petrol stations offer a fuel card that can be topped up and then used to make payments, a fuel card is usually a prepaid card that allows you to fill up on more favourable terms. However, with a petrol station loyalty card, you can collect loyalty points for the fuel you fill up, which you can then use to get a benefit - either a discount on the price of fuel or free snacks etc. The fuel discount cannot usually be used when paying with a fuel card. Discounts and other benefits can be redeemed when paying by another method (most commonly credit card or cash).
With few exceptions, such a fuel card can only be used within the domestic network of the petrol stations. Through fuel cards, petrol stations incentivise customers to fill up primarily with their fuel.
So if you are a private individual and want to save money on petrol, a fuel card from a petrol station in your city may be a good option for you. However, companies with larger fleets look for a slightly different product under the term fuel card.
Fuel cards for non-business (B2C) customers are offered by various companies - you can top up the money on your card and then pay at the stand with a discount.