What is the difference between a Wight, White Walker and an Other?

Also White Walkers=The Others, they are called White Walkers in the show because the writers were afraid that they would be confused with the Others of Lost.

Wights are corpses reanimated by some dark power or magic. They're vulnerable to fire or by being generally hacked apart and destroyed. They form the army of the Others.

The Others and the White Walkers are the same - White Walkers is the term more commonly used in the TV series because they thought Others might be too confusing. They're far rarer than the wights, and are more leaders than common fighters. They aren't vulnerable to fire but can be killed using dragon glass and dragon steel (theorised to be Valyrian steel). In the TV series, it's claimed that they're made by transforming live babies, and that they're led by an Other titled the Night King whose death would defeat the entire army, but neither of these have been confirmed so far in the books.