These nouns have related but very different meanings.
Prudent simply means careful, in a wise way—wisely cautious. It has very positive connotations:
It is prudent to save money for a rainy day.
Prudish has a culture-specific meaning—not all cultures have prudishness. Prudish means “avoiding and upset by discussions, images, or behaviors related to sex.” A prudish person might be upset even by talking about the human body in a science class, or seeing art that shows nudity. Prudish people may be easily disturbed by anything related to sex at all.
Not all cultures have prudishness (does yours?). In America and England, prudishness has a long history, associated with Christianity and the first English migrants to America, the Puritans, who were very prudish indeed.