Current draw of through hole LEDs and LED strips
You're totally right that you have the same current running through every LED when they're connected in series. Your confusion comes from not knowing how the typical LED strip is constructed. I have drawn one possible construction here:







simulate this circuit &ndash; Schematic created using CircuitLab

Each LED in the first column will draw I1 amperes, each LED in the second column will draw I2 amperes, etc. The longer your LED strip is, the more "columns" it will have. Thanks to Kirchhoff's current law, the individual currents will be added together to form I0 in my schematic. That's your total current.

They could have constructed it as one long series-connected chain. For a LED strip with 200 white LEDs you would need to feed this with about 600 volts. This is completely unpractical, even if the amount of current is low.