The correct answer to this open question is the following.
These are the two similarities and two differences between the war between the Persians and the greeks vs the war between the British and the American colonists.
Similarities.
1- Greeks defended their nation and territories. American colonists wanted to have their own nation and be independent of any other external nation, as was the case of Great Britain.
2.- Despite any difference, Greeks and Spartans united to fight against the common enemy: the Persians. The same happened in the 13 colonies. Despite differences, the colonies united to start the Revolutionary War of Independence.
Differences.
1.- Persians wanted to conquer new lands to increase the power and dominion of the Persian Emperor. British did not try to conquer any new lands. It already belonged to the British crown.
2.- With the possible victory over the Greeks, Persians contemplated the idea of enslaving the Greeks to be servants of the Persian Emperor. The British never thought of making the American colonists, slaves., just subdits, that is why the English king imposed so much heavy taxation on the colonies.