Although the two trees look very similar and are often confused for one another, they are genetically quite different. Mānuka (leptospermum scoparium) is also found in some parts of Australia where it goes by the name Jelly Bush. Kānuka (kunzea ericoides) on the other hand, is endemic to New Zealand, and is not found anywhere else in the world.
For a detailed description and comparison of the physical differences between mānuka and kānuka, take a look at chapter 2 of The Mānuka & Kānuka Plantation Guide, which you can find by clicking on the link.
The most commonly understood difference between mānuka and kānuka is the height to which they grow. Mānuka can grow up to 8-10m tall at maturity whereas kānuka can reach heights of 20-30m. Kānuka is a faster growing tree, and can survive in taller forests thanks to its added height. This allows kānuka to outcompete mānuka and live for longer periods of time.
Fun fact: most firewood that is sold around New Zealand as mānuka is actually kānuka.
Mānuka is much better at surviving in inhospitable conditions such as salt-ridden coastlines and low-nutrient soils. As a result, mānuka is more widespread throughout the country than kānuka.
The chemical composition of honeys and essential oils that come from mānuka and kānuka differ quite significantly.
Mānuka honey contains a compound called methylglyoxal (MGO). MGO kills antibiotic resistant bacteria such as MRSA, and also has powerful anti-inflammatory properties.
Kānuka essential oil is a lighter essential oil that has more monoterpenes, and does not contain any triketones. Because of this, kānuka oil absorbs faster into the skin and turns into vapour more readily, which makes it great for massage and aromatherapy.