Lucius Malfoy's lapdog?

I don't really get what the reltionship between Malfoy and Snape.
Sirius called Snape "Lucius Malfoy's lapdog". And Umbridge कहा something like "and Lucius Malfoy always speaks so highly of you!"
I get that they were/are both death eaters, and that Malfoy was a prefect when they entered school, but i still don't understand.
Narcissa कहा that Snape was an old freind of Lucius's, but i didn't think Snape would ever consider him a friend.

What's their relationship? Is it a one-sided kind of aquantinship? या is Snape just a friend of the whole Malfoy family?