As above.
The 700 is the 700mm approx outer diameter of the tyre. 622 is 622mm diameter of the rim where the tyre sits. So a 622 wheel is the same as a 700 wheel and you might see both of these quoted on rims/tyres or innertubes.
The 23 is the width of a tyre -you have 23mm width tyres. Manufacturers make one tube to fit a range of tyre widths - so you get 622 x 18/25 which means that they will fit all wheels with a 622 dia and widths between 18mm and 25mm