Tax is the driving force behind 'offshore', but for the great majority of well-off individuals considering offshore investment, tax is not directly an issue. They reside in high-tax areas such as the EU, the US, Canada or Japan, they pay their taxes, and if they make 'offshore' investments, it is in pursuit of higher returns, and without any intention to evade taxes in their home countries.
Some investors are outside the jurisdiction of high-tax areas, either because they live elsewhere, or because they are temporarily non-resident for work reasons. Such investors can often avoid having to pay taxes on their investments, whether on or offshore, but that is due to the investor's circumstances, not the location of the investment.