Although we have different definitions for love and compassion, and during tonglen practice love and compassion are practiced at different times, actually, they are not separate.
Just as smoke is a sign of fire, and with fire there is smoke, so, too, where love is present, so is compassion. In practice they come together.
When you are wishing to take on the suffering of others sincerely, then you are also wishing for their happiness. And when you are wishing sincerely for others’ happiness, then you are also wishing to remove their suffering.
Although the thought of love and compassion does not arise simultaneously, in practice they appear together.