Using the word "visit" implies spending time using the features of a website. Using the word "access" implies being able to reach it and gain entry, but not choosing to spend time on it. For example, you might say, "I have access to that website, but I never use it".

Also, 'access' may imply the need for a password.

"visit" is less formal and more common "access" is formal, not used in everyday conversation, but used in writing