Splitting mauls and axes are very different - but they both have a place on the homestead.
If you're heating your dwelling with wood, you'll get very familiar with both of these tools. The maul is used for breaking into a large log of firewood, the axe to split it into manageable and burnable pieces.
You'll need both of these tools at various times, but the one you'll rely on is the axe. There are many different kinds, from double bitted (a sharp edge on each side), to tomahawks or hatchets to cut kindling.
None of these tools are recommended for throwing, if you're into that popular sport. The axes used for that are specially designed to be balanced when thrown towards a target.
Luckily, these tools last a long time, with care. To prevent damage to the handle of the axe close to the head, try to stand further back from the splitting block.
You can probably get by without a spitting maul, if your firewood supplier breaks into the biggest pieces for you when they deliver the wood to your house.
Or, go with the one tool that does double duty; the hybrid maul/wedge type, like the one shown above.
Double bitted axes were more popular in times gone by for actually felling trees. With two blades, less sharpening is needed.
Best of all scenarios, if you're able to get an electric splitter, this takes only a few hours to get through your entire years supply of dry firewood.
Then, when you go to bring in your daily needs, split the bigger pieces, if needed, with the axe, and you're done.
The different types of axes and mauls all have their proponents. Some people like those with fibreglass handles, which last longer and don't rot.
The prices range from cheap or free (found at yard sales or in the buy and sell) to quite pricey - just look at those in specialty tool stores online or in your town. Just because they cost more doesn't make them better, make your own judgement on what will work for you.