Explain what the Americans who went westward and the Europeans who came to America had in common?

There is very little that all Native American people have in common. The thing that all native people have in common is bad experiences with colonial European powers who created the modern nations in North America. All have lost land and many lost much more such as lives, language, wealth, power and culture..

All people in North America had never been exposed to European diseases and all had huge losses in population until they gained immunity or in some cases until modern medicine.

Other than that, there were hundreds of languages and cultures that operated many different ways. Even in a small area such as the current State of California there were 78 different and mostly unrelated languages. People differed in economic, politics, beliefs, taboos, religions and deities, trade practices, agriculture, technology, values, food sources, attitudes towards war and conflict, modes of travel. size of tribe and many other ways.

There was vastly more variation in North America between cultures than there was in Europe at the time of first contact. Europe was mostly all feudal nations or empires. Mostly all one language family, one religion, all agricultural based with ruling urban areas and all monarchies. The area that has the US today had close to 300 languages in about 29 families and 27 isolates. There was no single religion or set of values.