Is water the same all around the world?

No. The H2O molecule undergoes isotopic fractionation at every step of the global water cycle. The isotope composition of both oxygen and hydrogen changes during evaporation of ocean water, condensation of air humidity in clouds, exchange between water and atmospheric water vapour during transport in clouds and during precipitation. Therefore the isotopic composition of precipitation (rain, snow) around the globe varies depending upon several parameters, such as latitude, distance from the ocean, source of water for precipitation, altitude and the temperature. Generally, the δ2H and δ18O values of precipitation decrease with distance from the sea and with altitude, but they also change seasonally: they are lower in astral winter (at low temperature) and higher in astral summer (at higher temperature). Each region of the world has thus a typical range of δ values of precipitation; however, there is no universal formula to calculate the δ2H and δ18O values for each particular spot on Earth.