Since the European Directive on Personal Protective Equipment came into force, equipment deemed to be "safety" has to bear the CE mark, showing that the manufacturer has achieved a required standard in production, testing and quality control. How it affects ice axes is somewhat muddy, given that the actual standard to be adopted is still only provisional. What is certain is that CE marked safety equipment must come with technical instructions, and an explanation of its intended use. 

THE HEAD 
Back in the classical days of hob-nailed mountaineering, the adze was an important feature, used to cut steps. Crampons have taken away much of the need for step cutting, but it's still handy to be able to swipe lumps out of packed snow and ice, particularly when it's all you've got to dig that emergency bivvy!

Compare a climbing axe with a walking model, and you'll see that the climbing pick is more acutely angled. A climber wants it to bite first time when he whacks it into the ice. But a walking pick is primarily an emergency brake, used for self arrests after you've lost your footing. A steeply angled pick would be more likely to snatch out of your hands, so the walker's version is almost perpendicular to the shaft, with just the merest curve, designed for safe progressive braking. Mountaineering models may have a slightly more pronounced curve and teeth, handy for steeper terrain where putting the pick into the snow can give you a useful handle to help you up. 

THE SHAFT 
Axes for walking/mountaineering come with longer shafts than climbing axes, providing a certain amount of security as a "third leg". Held by the head, this is the way it'll spend most of its time in your hand. 
The easy way to determine the length correct for you is to hold the axe by its head, arm loose by your side. The point of the spike should be around two to three inches above the ground. Any longer and it'll be unwieldy - shorter isn't recommended for beginners, although you may see more experienced mountaineers with shorter ones. Sizes range from around 50cms, stepping up in 5cm increments to 70 or 80cms - sometimes more, depending on the make. 

GRIPPERS 
Budget axes or purely walking models may not necessarily have grippers - those that do will have a moulded rubber or plastic sheath on the lower part of the shaft, either texturised or ergonomically shaped to provide some grip when you're holding that end. 

LOOPS OR LEASHES? 
Some use loops to remain attached to their axe in the event of a momentary slip of the hand, some use longer leashes - others prefer not to, but there are plus and minus points for each. 

Sliding wrist loop 
Pros: Enables you to stay in contact with your axe whether you're holding it by the head or shaft. 
Cons: You need to change the loop over to the other wrist every time you change hands to keep the axe on your uphill side. Some contend that keeping the axe on a loop or leash means there's a greater chance of being injured by the axe if you lose your grip on it when you're sliding. (But you will anyway if you lose your axe during a slip). 

Leash 
Pros: With a longer webbing leash attached to the head of the axe, you can either keep the wrist loop permanently on one wrist - it's long enough not to need swapping over every time the axe changes hands - or you can attach it to your rucksack waist belt. 
Cons: With a bit more dangling about, you need to take a little extra care not to get it tangled with anything, particularly if you're roped up. 

Neither 
Pros: Greater freedom to swap hands quickly. No chance of getting whacked about the head by a flailing axe if it's wrested from your grip during a tumble... 
Cons: ...but hang on a second, is that the top of a crag I'm sliding towards?