Specifically in Shakespeare's Macbeth, we see brotherly love between Macbeth and Banquo, and erotic love between Macbeth and his wife Lady Macbeth.
Macbeth is a decorated soldier for, and supporter of, King Duncan of Scotland. However, Macbeth is extremely ambitious, and the witches that he meets near the battlefield at the play's beginning, convince him that he can be king. Macbeth loves Duncan and has served him well. He is torn between killing Duncan and jeopardizing the good life he has.
When we see Lady Macbeth and Macbeth together for the first time, the passion between them rests beneath the surface. He refers to her as "his dearest love." Their devotion is obvious, but the tension between them is sexual, and they struggle for the upper hand. I believe the erotic nature of their love goes beyond simple affection. They know each other well. It is logical to assume that the strength she conveys with regard to killing Duncan is an extension of who she really is, and sheds a light on the relationship that exists between this husband and wife.
They are evenly matched it would seem: Macbeth is a fierce and highly acclaimed warrior, by no means a coward. His wife is as ambitious as her husband, and appears to have a strong, masculine spirit: she wields a power over Macbeth, but only when she questions his bravery. There would be no "roses and candy" relationship with these two, but a fiery meeting of body and soul that draws them always closer, until they seem almost of one mind.
The British actress Sarah Siddons, one of the leading tragic actresses of the 18th century, wrote that in her interpretation, Lady Macbeth has at once subjugated all her femininity to ambition, and at the same time maintained her feminine attractiveness to Macbeth. 'Such a combination only, respectable in energy and strength of mind, and captivating in feminine loveliness, could have composed a charm of such potency as to fascinate the mind of a hero so dauntless, a character so amiable, so honourable as Macbeth.'
In terms of brotherly love, Banquo and Macbeth are best friends, like brothers. The two men have fought side-by-side. They are on the heath when the witches arrive and give Macbeth the predictions that motivate him to kill Duncan. They give Banquo three predictions as well, but he ignores them, seeing the witches as messengers from hell.
Because Banquo is a witness to what the witches have said to Macbeth, Macbeth knows he must kill Banquo after Duncan's death, before Banquo figures out that Macbeth has murdered the King. Macbeth plots to kill Banquo and his son Fleance; Banquo is murdered, but Fleance escapes.
It is Macbeth's ambition that turns him into a tyrant. Ultimately, he is brought to justice, killed by Duncan's son, Malcolm.
The difference between these two kinds of love seems rather straightforward. The friendship between Macbeth and Banquo comes from years of fighting along side each other, and protecting each other in battle. There is a strong trust that has developed based on the dependence present when one has your life in his hands.
Erotic love in this play seems a less supportive kind, and more competitive between Macbeth and his wife. There seems less trust here: they are comfortable with each other, but their relationship seems based more on fire and jockeying for mastery, and less on protecting one another. Could a warrior and a woman capable of murder be anything but passionate?