I have SharePoint 2013 on-premise application where we have two application servers (windows server 2012 R2) in chich Central administrator is installed and our application also hosted on the same server. We have a proposal that, moves this setup to the cloud. I checked all the article from Microsoft, they mentioned about the tool but nowhere I got a clear idea of what to choose whether SharePoint online or azure (Office 361). I need guidance on how could I achieve this migration to the cloud.
Assuming you have a fairly standard SharePoint deployment without a lot of custom applications and custom integrations to other systems then the choice is simple; move to SharePoint Online like most others do.
You'll need a migration tool to migrate existing SharePoint 2013 sites to new sites in SharePoint Online. Check out the Microsoft SharePoint Migration Tool.
Moving to Azure would still require you to build out and maintain your own SharePoint server farm on Azure Virtual Machines. Not something I can recommend unless strictly necessary.