They can be, but they don’t have to be. Painting doors and trims the same colour as the walls creates a calm, modern, almost seamless look, especially if you use a slightly different sheen (for example, matte on walls and satin on trims). This works well in small rooms because it reduces visual breaks and can make the space feel larger.
On the other hand, using a contrasting colour – classic white trims with coloured walls, for instance – frames the room and highlights architectural details. It’s a more traditional approach and can look very sharp if you like that style.
The main thing is consistency. Whatever you choose, repeat it throughout the home as much as possible so doors don’t look random from room to room. If you’re unsure, white or off-white trims with coloured or neutral walls are a safe starting point that suits most styles.