Do homing pigeons and migrating birds have the same 'instincts'?

Both, but mainly instinct. My Father was a pigeon fancier. He trained, raised and raced birds as part of a concourse.
The furthest race they did was 500 miles, but I am sure there are recorded flights home that are much further.

Most give the ability towards an acute sense of smell.

Instinct, amplified by genetics, mostly.

“The homing pigeon is a variety of domestic pigeon derived from the Rock Pigeon (Columba livia domestica) selectively bred to find its way home over extremely long distances.[1] The wild rock pigeon has an innate homing ability,[2] meaning that it will generally return to its own nest and its own mate. This made it relatively easy to breed from the birds that repeatedly found their way home over long distances. Flights as long as 1,800 km (1,100 mi) have been recorded by birds in competition pigeon racing.[3]”

Wikipedia

I was curious about the answer to your question and I remembered reading a book recently where some pigeon flew an incredible distance in a wounded state to come back to its roost. I tried to find the book but I can’t remember the title. In searching for it I came across this book. Like marinelife says it is partly instinct but since the birds have been bred for this so long the genetic inclination has been magnified and enhanced quite a bit. Start on page 185 in the excerpt and it cites some cool statistics.

“Charles Walcott, recently retired dean of the university faculty at Cornell University and former director of the Cornell Lab of Ornithology, calls racing pigeons the athletes of the bird world. “They have about twice the muscle mass that your common street pigeon does,” Walcott says. “If you grab a regular pigeon off the street and take it a few blocks away, it will find its way back to the general area because they’re quite territorial. But it may stop and linger at the nearest statue or the local McDonalds.”

Walcott and others established that the earth’s magnetic field is one of several cues homing pigeons use to orient when released in unfamiliar areas. They also use the angle of the sun, polarized light, star patterns, and olfaction. Individual pigeons prioritize their cues differently, based on where they were first trained. They also have individual quirks. Walcott mentioned one pigeon that was trained near a mountain. When released, it always flew to the nearest mountain regardless of the direction of the home loft, and found its way from there. Another “was very good at navigating but terrible at finding the loft. He’d come down and find somebody gardening, then land and look helpless. He had a label on his back to please call collect and we’d get a phone call and go out in the car and bring him home.”
more

Scientists aren’t positive about how this works, but there are many theories about the magnetic sense of birds. There are two main models: a radical-pair based model and an iron-mineral based model. This sense is used for migration and navigation, and other animals with magnetic sense include salamanders and newts, sea turtles, eels and fishes
On the iron-mineral based model of magnetoreception:
Fleissner et Al. 2007 concluded that there are two kinds of iron-based minerals in beaks, Magnetite (Fe3O4) and maghemite (Fe2O3). There are six patches in beak where iron minerals are concentrated, minerals are in the dendrites of neurons, on inner lining of upper half of beak.
How it works (speculations)
Magnetite forms micro clusters attached to cell membrane, maghemite has plateletlike structure arranged in chains inside dendrite1.
magnetite is ferromagnetic, senses the extremely faint magnetic field, maghemite platelets amplify the signal. The structure also contains an iron vesicle, the exact function of which remains unknown.
Here you have a close-up of these structures: http://tak-dev.appspot.com/lex/plos-paper_files/g001_m.png

Radical-pair based model
Involves a chemical reaction in the eye of the bird, which involves a radical pair.
A radical pair is a pair of molecules that each have one unpaired electron, making it sensitive to magnetic fields. In certain situations, the magnetic field can affect the products of the reaction.
Radical-based model: theory
Suppose products of the reaction affect the sensitivity of light receptors, resulting in brighter or darker regions in vision. It is known that the reaction affects light-sensitive chemicals called cryptochromes that are sensitive to blue or green light.
Ahmad et Al. shows that the sensing of magnetic fields works properly in blue light, but not in red light

Compare this system (or systems) in birds to an MRI, which is made up of a large superconducting magnet that creates a stable field and 3 smaller gradient magnets to create a variable field and allow portions of body to be scanned

So with this great sense that birds have, what can go wrong when navigating?
Well, many things. The bird could get eaten. Or they could be led off course:
Flamingos in Siberia- http://www.npr.org/blogs/krulwich/2011/03/07/134229725/flamingos-drop-from-siberian-sky-locals-mystified

Sorry if this is really technical, but I did take a class on neurobiology last year and thought I would share my knowledge! We got a project in that class to do a short presentation on senses of humans (or, in my case, other species- for me, birds! yay). Otherwise, I would not know the answer to your question.