You must be thinking about the difference between these two ways of Account Live password reset. Well, both the methods lead to the same destination; however, the way of resetting the password is different in these two. You can choose the first one if the Microsoft account has the two-step authentication feature is on.
On the other hand, account.live.com/acsr needs to be visited if the feature is disabled. To reset Account Live password, use either your registered email address or phone number at https://account.live.com/password/reset, or an alternate email address at account.com/acsr.
In case, if you do not have an alternate email, then create a new email with Outlook.com, and the option for signing up for a new ID is given at the password reset page only. For further information on Account Live password reset process, you can contact Microsoft customer support team at 888-315-9712.