Does all woodwork need to match?

While wood finishes don't need to match, they should complement each other. Look at the color bias of each wood to see if it is warm or cool, then make sure their undertones match, regardless of finish.

Does all the trim in a house have to match?

As a general rule, plan to paint all the trim throughout the main areas of the house the same color to create a unified effect from room to room. In more personal spaces, such as bedrooms and bathrooms, you might want to play around with more unique wall and trim color combinations.