Wikipedia says we're both right. They have different lengths, and once upon a time anoraks didn't have full length openings:

"An anorak or parka is a type of heavy jacket with a hood, often lined with fur or fun fur, so as to protect the face from a combination of freezing temperatures and wind.

This kind of garment was invented by the indigenous inhabitants of the Arctic region, who needed clothing that would protect them from windchill and wet while hunting and kayaking. The word anorak comes from the Greenlandic Inuit anoraq, while the word parka is of Aleut origin. Underneath the anorak the Inuit wear warm clothes. Inuit anoraks have to be regularly coated with fish oil to keep their water resistance.

The words "anorak" and "parka" are now often used interchangeably, but when first introduced they described somewhat different garments, and the distinction is still maintained by some. Strictly speaking, an anorak is a waterproof jacket with a hood and drawstrings at the waist and cuffs; while a parka is a knee-length cold-weather jacket or coat, typically stuffed with down or very warm synthetic fibre, and having a fur-lined hood. Originally an anorak specifically implied a pull-over jacket without a zipper, button or frogged opening, but this distinction is now largely lost, and many garments with a full-length front opening are now described as anoraks."