No, it doesn’t mean that you have to have a different merchant account for each website.
A merchant bank is responsible for your transactions to a certain extent, so they are essentially granting you credit for your business. So, they want to know what type of business you are in before they decide to take on the risk of processing your credit card transactions.
You should check their policies and terms regarding additional websites or product lines. There will certainly be some high-risk niches that they will not allow, so as long as you do not start selling prohibited products you should be okay using the same merchant account for multiple websites.
Again see the terms and conditions of your current merchant bank to see what restrictions they have in place.