What is the difference in treatment of a broken or sprained little toe?

Toe injury. Treatment of both are essentially the same. You may "buddy" tape your small toe with the adjacent toe which will act as a splint. Also, it would be beneficial to wear a stiff/supportive-soled shoe to protect from too much motion while walking. Fractures will heal within 3-4 weeks generally and most likely sooner for a sprain.
Bone vs soft tissue. A broen toe means a fracture of the bone, a sprain is a tendon or ligament injury.
Very little. Whether broken or sprained, an injury to the little toe is treated with conservative measures: taping, wearing stiff soled shoes to prevent bending, and taking some over the counter anti-inflammatories. What you get out of the xray is a prognosis: you'll know how long it takes to heal. A week or so for a sprain, 3 weeks or so for a fracture.