Statutes refers to statutory law while amendments is a short-hand reference to constitutional amendments. Basically the difference between the U.S. code (most all of the laws Congress passes) and the U.S. constitution with its amendments. States have their own constitutions and bodies of statutory law.
Initiatives are subdivided into direct (people voting on the law themselves) or indirect (forcing the legislature to vote on it) with some states like Washington having both direct (initiatives to the people) and indirect (initiatives to the legislature) initiatives.
Referenda has two types: veto referendums (citizens gathering signatures to contest and vote on a law passed by the state legislature) and legislative referrals (the state legislature referring a measure to the citizens to vote on).
So for the purposes of that map:
Blue = Citizens can initiate statutory law and state constitutional amendments.
Green = Citizens can initiate statutory law but not state constitutional amendments.
Yellow = No statutory or constitutional initiatives but allows for veto referendums.
Orange = Only state constitutional initiatives (no statutory initiatives or veto referendums).
Tan/white = No statutory or constitutional initiatives and no veto referendums.
I think all 50 states have the ability for legislative referrals (most tend to be constitutional referrals but they can also refer statutory measures) and I'm pretty sure all the states in blue and green allow for veto referendums.
It can be pretty confusing, I had to look up all the terms when I was first confronted with them. This page has a good overview of each state's direct democracy laws:
http://ballotpedia.org/wiki/index.php/Forms_of_direct_democracy_in_the_American_states
