I think cookie is used in the US and buscuit is used in the UK. Where I live, cookies are what we eat as a snack and buscuits are what we give to dogs generally. (edit:Typo)

They generally mean the same thing. There are many loan words (words borrowed from other languages) in English. Biscuit comes from French, and cookie comes from Dutch. There are lots of examples of different loan words being used in different Anglophone countries. Another example would be: zucchini and courgette (Italian - North America, French - UK). When talking about the sweet, round food - cookie is used in North America and biscuit is used in the UK. I would imagine Australia, New Zealand, etc, would say biscuit. Due to globalization and US influence, you see the word cookie used a lot in the UK. An example would be 'chocolate chip cookie' or 'cookie dough ice-cream' in the UK.

Cookies are american!

Technically, a cookie is baked once from dough, and a biscuit is baked, cut, then baked again. "Bis-cuit" literally means "cooked twice". In reality, it's more of a regional difference, as other commenters have said. In Australia, we have the "ANZAC biscuit", which is connected to our military service (this needs a whole other discussion to explain it, but for now you just need to know that it exists). If you look at the recipe, you'd say "well, it's a cookie!" However, we've specifically chosen to call it a biscuit, with the intention of, "please don't call it a cookie." :)