For example, if 90% of the sun is covered by the moon, then only 10% of the usual amount of sunlight will light up the area around you. So it is quite a bit darker than usual.
However, the portion of the sun that is still visible is just as bright as it would be on any other similar day. If you stare at that remaining portion of the sun, or aim a camera at it, it will cause the same damage as it would any other time, only in a smaller crescent-shaped area instead of a full circle.
The danger to your eyes is even greater, because the overall darkness tricks your irises into opening up wider and letting even more light in than usual.
You're pretty unlikely to stare at the sun for 30 seconds on a normal day. But people do that during a partial eclipse, and that's the problem. Similarly, people don't usually aim their cameras directly at the sun with the lens wide open and no solar filter - except during an eclipse.
A total eclipse is quite a different thing, of course. During totality, the sun's bright photosphere is completely hidden, and only the much fainter corona is visible. This is only about as bright as a full moon, and it's perfectly safe to take pictures with any lens, and to observe directly with the naked eye - even with binoculars.
Anecdotally, I viewed the 1979 total eclipse with binoculars (and no filters), and at the end of totality I continued to look through them for a few seconds to see the diamond ring and Baily's beads.
It didn't harm my vision at all, even though there was some fair amount of direct sunlight coming through by then. But it was only a few seconds. The duration of sun exposure certainly is a factor.