Yes, some business savings accounts are only available to certain business types. For example, one type of account may only be eligible for a limited company or a sole trader, but not for a charity.
You can also have more than one business savings account if you wish. Just bear in mind that the more accounts you have, the more admin there might be in terms of opening and maintaining them.
And depending on the amount of spare money you have, you might not make the most amount in interest if you split your funds between several accounts.
Also, if your business is a limited company, you cannot use a personal savings account as a business account, because the business is a separate legal entity.
But you can if you're a sole trader, as your business and personal finances are considered one and the same.