The common link is that both are states of your mind and heart resulting from your actions and circumstances.
It is actually a matter of feeling and experience. Not an attitude by itself. An attitude that gets formed out of your feelings and experiences.
You get being bored when something is too much monotonous and does not give you pleasure or satisfaction. Rather, you get disliking and uneasiness at your state of affairs. You feel drowsy and sleepy also at it. You want to get out of it anyhow.
On the other hand, being content is a feeling of satisfaction that you derive on being at your state of affairs. You are positive, at ease and feel happy also at your position. You may see other better options, but you feel that you need not worry even if you don't get at them because of your content state.