No, Nike is not using the same sizing as Adidas or Under Armour. To see the differences, you can check the size charts for clothes and shoes on their websites. Some items may have similar sizes, but for example, the difference between shoes can be often called essential or "big".
When checking the sizes, please note there are usually different sizes for US, EU, UK etc. You can also check the sizes in Inches or Centimeters. This may be more reliable when comparing the clothes or shoes.
From my experience, Nike has larger size M for t-shirts and jackets, than other brands I prefer. Because of that, when I buy some Nike items, I choose size S instead of M.