We employ the Google and Apple mobility data to identify, quantify and classify different degrees of social distancing and characterise their imprint on the first wave of the COVID-19 pandemic in Europe and in the United States. We identify the period of enacted social distancing via Google and Apple data, independently from the political decisions. Interestingly we observe a general decrease in the infection rate occurring two to five weeks after the onset of mobility reduction for the European countries and the American states.