light vs lamp

For me:

Generally, a lamp is free-standing whereas a light is fixed to the wall/ceiling.

Got it. Simple and easy to understand. Cool.

I think "light" is even broader than that. It's anything that casts light. If I say "Don't forget to put out the light" I could refer to either a lamp or a ceiling fixture. Or "We'll be home after dark, so let's leave a light on" could refer to either.

I see. Thanks, GG.

I don't disagree that lamps are often free-standing, but a Google image search for "wall lamp" (for example) shows that they don't have to be.

To distinguish in these cases, a "lamp" to me suggests something that gives out softer/more "ambient" illumination, has a fancier or more expensive design, or is designed for a specific purpose.

I think there is a difference here even though the two words are very interwoven. A lamp is a device that gives light. It still remains a lamp even if no light. Light on the other hand is a heat energy or an electromagnetic wave that gives illumination. The sun, the moon, fire, electricity etc, are all means of generating light and cannot be called lamp. So lamp is a device to generate light whil