Early Discovery
Discovery is a broad term used to describe many of the activities related to investigation: understanding the problem, the people affected by it, evaluating and testing viable approaches, and determining a solution – but not actually building it.
Discovery should be continuous throughout the lifetime of a project, so we'll refer to the initial phase at the very beginning of a project as "Early Discovery";
Discovery Projects
Sometimes we have projects that precede an implementation called a "Discovery Project". The purpose of these projects is to better understand what could and should be built, at a high-level, and set up the following project for success. The methods vary, and can involve a variety of activities, including ideation, journey mapping, story mapping, prototyping, and more.
While these projects often front-load something called discovery ahead of something called delivery, don't confuse this with "big upfront design". We are not making decisions here at the detailed feature level and are much more interested in the what than the how. We are focused on ensuring that we are headed in the right direction for product development and the outcomes of a discovery project should be focused on setting up the following project for success.
It is worth mentioning that projects that follow early discovery work will have continuous discovery throughout -- discovery is not complete when an implementation starts.