Single moms are often single because of emotional dissatisfaction with the marriage and initiated the divorce or had unprotected sex with an unreliable partner. Single dads are often in custody of children because the mother died or was so insanely cracked out and abusive the state actually gave them custody.

That is to say, single moms are often by choice (or fucking out of wedlock for fun or to try to capture a randomly selected guy). Single dads are often not.

That doesn't cover all cases, but is the broad impression of the two types I think.