If you enter your credit card details into an online shopping account then this account has your credit card details and so does anyone else who accesses your account.
Although credit card companies offer fraud protection it is sometime hard to prove your innocence if a criminal has your card details and clones them.
Many people consider that using Paypal for online purchases is safer than entering your credit card details onto a site you may only use once. This is because the payment is made securely but your credit card details are not revealed to the seller.
Think carefully before buying anything on a site you do not know particularly if the site offers a bargain price. Many of the sites are run outside of the jurisdiction of the United Kingdom (China and Russia) and are directly operated by criminals who will take your money but not supply any goods.
Most legitimate sites offer you the opportunity either “to save” or “not to save” your credit card details “for future purchases”. This tick box can be obscure and small but don’t save your credit card on sites you do not use regularly. Use PayPal if you can.