“Grow light” isn’t a technical term, nor is it a unique piece of technology. Any light can be a “grow light” since plants really aren’t that picky about where the light comes from.
What sets grow lights apart from regular lights is the spectrum of light they emit when powered. Your typical lamp uses “soft” and/or “warm” light (which are terribly vague, informal descriptors of light quality and intensity). They tend to be yellowish and fairly weak as far as lumens (light power) are concerned.
Grow lights are often (but not always) “full spectrum” lights. That means they contain the full visible spectrum of light, from red to violet, plus a little extra on both sides – a touch of ultraviolet light can be beneficial. These lights are often described as “white/blue” or “cool” or “daylight”.
So, no, they don’t function any differently than other lights. The spectrum a lightbulb produces is determined by the components with which they are manufactured.