Do fractured finger or toe bones always turn into arthritis?

Not always: In instances where you have a slight fracture (hairline fracture, small stress fracture) in proximity to a joint but not involving the joint per se, the healing may be complete and without sequelae. If a fracture involves the articular surfaces of a joint, is displaced or if there are other factors (e.g. Osteoporosis, infection) then arthritis commonly follows.

No,: No, if it is a simple fracture. Arthritis develop in any joints after fracture mainly due to 3 reasons, (1) fracure due to high velocity trauma (which is rare for finger or trauma) (2) fracture involving joint and cartilage (3) if fracture is communited meaning multiple pieces where bone alignment will never gonna be normal again even after fixation.

Not always: For a fracture to cause arthritis generally it needs to involve the joint surfaces of the bones that make up the joint. If the fracture occurs away from the joint surface then the chance of arthrtis is low. However if the fracture results in a healed but poor alignment of the bone away from the joint then it may abnormally wear the joint surfaces indirectly resulting in arthritis of the joint.

No: Fractures that commonly lead to arthritis and joint problems are those that extend into a joint. Thankfully, they are a minority of fractures.