In a nutshell:
LiveCycle Designer is a tool for creating PDF forms, form templates (XDP format) and form guides.
LiveCycle Forms is a server side product for combining form templates and XML data to produce interactive PDFs or form guides. It also can process submitted forms including extracting data from a template. Forms can be combined with other LiveCycle modules to create a more complex document workflow.
In other words: You build the template with Designer. You use Forms to merge the template with data and process user submissions.