In the US and much of the world, ugg is a trademark not a description of a specific type of footwear.
In Australia, an ugg boot is always a sheepskin boot and an Australian icon. Because I live in Australia, I buy and wear locally made sheep skin boots and the companies selling them solely within Australia are allowed to call them ugg boots. My Australian made boots are wonderful.
The trademark for the word ugg was registered in the US and 130 countries by a US company and now Australian companies calling their boots ugg boots for product sold outside of Australia are being sued for trademark infringement, which has been upheld by US Courts. The action is yet to be determined within the US Supreme Court:
Ugg boot maker says federal government support could help take case to US Supreme Court - ABC News
Australian ugg boot maker loses trademark appeal against US giant Deckers - ABC News
Lesley, if you want a sheep skin boot, it would be best to search for that specific description as Australian companies producing what was formerly called ugg boots don't want to be sued for selling them to you. I have bought this brand and highly recommend their product:
Premium Quality Sheepskin Boots for Men | EMU Australia