While credit card fraud is a hugely stressful crime to fall victim to, these schemes typically won't provide the scammer with access to your bank accounts. This means your other accounts won't be at risk, but there are other ways criminals may attempt to gain access. The most common of these is the theft of your personal information, usually through emails, texts or phone calls that pretend to be from your bank.
This approach is known as 'phishing,' and it's easy to fall victim to if you're not aware of the dangers. Common signs of a phishing scam include calls from a bank that you're not a customer of, emails that include links where you must enter your personal information, and messages that do not refer to you by your full name or an identification number.
If you're ever in doubt about the validity of a message, it's always best to contact your bank directly and ask. If all is above board, they'll be able to quickly let you know, giving you peace of mind that your personal details are safe.