just a protip here. you don't go round calling your partner a lover. it's slightly disrespectful.
Eng. equivalent "My better half"?
애인 is just someone of your affection (intimate but no physical relationship). 연인 has a more serious meaning (prob. closer to "lovers").
So describing 애인 as significant other seems a bit of an exaggeration, not?
It is really just a flowery way of describing 남/여자친구, is it not?