Ambient means the light meter is designed to meter light from a continuous source like the sun. The alternative to ambient metering is flash metering, which measures the short bright pulse of light from a flash (strobe). Most flash meters will also measure ambient.
Incident metering means you measure the light falling on you subject, rather than the light reflected by your subject. In order to do this, you need to be able to meter where your subject is - easy enough for most portraits, but not so easy if you are shooting a distant mountain.
The alternative to incident metering is reflected light metering, which measures the light reflected by your subject. This is convenient for distant subjects, but can be tricky with high contrast subjects as the reading depends on how much of the bright areas and how much of the dark areas the meter sees. A spot meter solves this problem by metering from a very small area of the subject.
Personally I prefer incident metering for nearby subjects, unless they are especially tricky, in which case I may use spot metering. I generally use spot metering for landscapes.
An 18% gray card allows you to measure incident light with a reflected light meter. I think it's easier just to use an incident meter (with the dome).
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