1) to love romantically
Naturally, yêu only means "to love romantically". However, it should not be surprising that one can easily find that it also means "to love non-romantically" in awkward translation from other languages.
1) (unromantically) to love
Ba thương con vì con giống mẹ
Mẹ thương con vì con giống ba
Cả nhà ta cùng thương yêu nhau
Xa là nhớ, gần nhau là cười
Daddy loves ya 'cuz you're just like your Mommy
Mommy loves ya 'cuz you're just like your Daddy
And we all love each other
We miss each other when we're apart, we smile at each other when we're together
2) (Southern Vietnam, colloquial, euphemistic, romantically) to love
1) to love, to like
In the north, yêu appears to use for both. I'm not 100% sure on this. I feel the sentence above is just a google translation.
In the south, thương is for both romantic (with less intensity) and platonic love while yêu is only for romantic love and only between humans. So the sentence above would be thương in the south.