The difference between Dyson DC59 and DC62 may be the model number.
If you visit the official websites of Dyson for different countries, you can find that the markets that have the DC59 available do not have the DC62, and the countries where you can find a DC62 do not sell the DC59.
And if you compare the features and specs of these 2 Dyson cordless vacuum cleaners, you will find that they are almost the same unit. For example, they both feature 350W Dyson digital motor V6, 2 Tier Radial cyclones, improved motorized head with carbon fibre filaments, re-engineered nickel manganese cobalt battery to provides more power than previous models, etc.
So, I think they sell the same unit with different model numbers to different markets. For example, at Dyson AU websites, you can find the DC59 www.dyson.com.au/vacuumcleaners/handstick/dc59/dc59.aspx; at Dyson CA you will find the DC62 model http://www.dysoncanada.ca/en-ca/vacuumcleaners/cordless/dc62/dc62-animal.aspx
Do you know more details about them? If yes, please share with us by commenting below.