Sea level fluctuations aren't directly related to rainfall, so your second guess of a bucket is nearer the mark. Of course they aren't really buckets. Rainfall is caught in standardised containers called gauges. Things are getting more sophisticated, though, wih rainfall being measured by radar, sonar and microphones which are used mainly in oceans where using a gauge is a little more difficult. Measuring rainfall must be relatively straightforward because you can volunteer to take readings outside your own home for the Met Office without having any formal qualifications.