Can someone explain in less than 2 sentences the difference between both? Yes, I know google can provide hundreds of answers but not one in 2 clear sentences:)
HTTP handler is the process that runs in response to a request made to an ASP.NET Web application. HTTP modules let you examine incoming and outgoing requests and take action based on the request.
HTTP handler is where actually compilation is done based on setting. such as if page extension is .aspx then it will compile through system.web.Ui.Pagahandlefactory. once compilation is done at HTTP handle request will go though HTTP module and IIS.