""What, precisely, is the difference between an infertile heterosexual couple adopting a child and making a caring and safe environment for it, and a homosexual couple (male or female) doing exactly the same thing?"

Of course there are differences.....between an infertile hetero couple...a fertile hetero couple...and a homosexual couple.

The first difference being a medical problem which stops the infertile couple performing their primary natural function, the second difference is that the homo couple are of the same gender and never designed by nature to produce children.
Almost all experts agree, that mother father children is the best template to bring up children.....simply because that is nature's design. Homosexual rearing is a dangerous, idiotic,social experiment, involving the wellbeing of young children, often with no say in whether they wish to participate or not.