Asimilarity between the leaders of state executive and legislative branches is that

There are similarities and differences between a parliamentary democracy and a presidential democracy. The United States has a presidential democracy, while the United Kingdom has a parliamentary democracy. This makes it easier to pass laws because there is no threat of a presidential veto in a parliamentary democracy. 
similarity is that in both forms of government, the people elect their representatives. This gives the people significant power since they are able to decide who will represent them.
hope this helps

They serve four year terms of officethey are usually elected by popular vote*they are responsible for making state lawsthey have budget-approval responsibilities