It is really hard to compare the two LED strings when you don't provide ANY information other than power and voltage requirements and the length of the strip. Post links to each of the two products and upload pictures and manufacturer's suggested wiring diagrams. Don't make us jump through your monitor screen and pull your teeth to obtain this information!
LEDs require DC voltage, not AC voltage, to operate. The amount of voltage required depends on how the LEDs are connected and the number of LEDs illuminated.
If one strip provides for operation from 120 V
AC line voltage, then there is additional circuitry involved to rectify and reduce the line voltage and limit the current to levels appropriate for LED operation. You didn't specify whether the 120 Volts was AC or DC.
If another strip provides for operation from 12 V
DC (a car battery for example), additional circuitry is involved to reduce the voltage and limit the current to levels appropriate for LED operation. You didn't specify whether the 12 Volts was AC or DC.
While both LED strips may consume the same amount of nominal power, or 25 watts in this case, they will have very different additional circuitry. Sometimes the additional circuitry is "built in" to the LED strip and sometimes it is external to the strip. Sometimes it is both. For example, consider the case of a "wall wart" that plugs into a 120 V AC convenience outlet and connects to the LED strip.
Most LED strips are manufactured with two DC power supply rails that run the length of the strip, one on each side. The power rails connect to integrated circuit LED current drivers interspersed between groups of two, three, or four LED emitters. This is repeated throughout the entire length of the strip, which may originally have been several hundred meters long before being cut to "three-foot lengths" or some other appropriate length. The advantage of this is economy-of-scale and a fixed power consumption per unit of length. There are many variations on this theme, such as RGB LEDs and color controlled LED strips.
Tell us what you have,
@kamas, and maybe we can tell you what the difference is between your "125 Volt, 25 watt" strip and your "12 V, 25 watt" strip.