Here's a glossary of the key objects in the code base related to search problems,
for your reference:
SearchProblem (search.py)
A SearchProblem is an abstract object that represents the state space, successor function, costs, and goal state of a problem. You will interact with any SearchProblem only through the methods defined at the top of search.py
PositionSearchProblem (searchAgents.py)
A specific type of SearchProblem that you will be working with --- it corresponds to searching for a single pellet in a maze.
CornersProblem (searchAgents.py)
A specific type of SearchProblem that you will define --- it corresponds to searching for a path through all four corners of a maze.
FoodSearchProblem (searchAgents.py)
A specific type of SearchProblem that you will be working with --- it corresponds to searching for a way to eat all the pellets in a maze.
Search Function
A search function is a function which takes an instance of SearchProblem as a parameter, runs some algorithm, and returns a sequence of actions that lead to a goal. Example of search functions are depthFirstSearch and breadthFirstSearch, which you have to write. You are provided tinyMazeSearch which is a very bad search function that only works correctly on tinyMaze.
SearchAgent
SearchAgent is a class which implements an Agent (an object that interacts with the world) and does its planning through a search function. The SearchAgent first uses the search function provided to make a plan of actions to take to reach the goal state, and then executes the actions one at a time.