Survey Sampling
Survey sampling is a procedure of selecting prospective respondents for a survey experiment.
Probability Sampling
Probability sampling begins with identification of the frame. A properly-specified frame covers the complete true population. An improperly-specified frame introduces sampling error.
A census is a survey of the complete frame. The probability of selection is 1, so the base survey weight is also 1.
Stratification
Stratification is the partition of a frame into discrete classes using information that is known for the entire frame. Each stratum is sampled separately, often with differing probabilities of selection.
Stratification qualifies as a complex survey design because the standard errors must be estimated with attention to strata. As an example, if a stratum happens to be excluded from an estimate, its contribution towards true variance is excluded from a conventional estimator. This is especially common with sub-population estimates, and this is why Stata supports subpop and over options for many estimation commands that can otherwise seem redundant given if expressions.
Ideally, stratification uses information that is known to be true, such that there is no reason for cases to be 're-classified'. Manipulating strata in such a way distorts variance estimates.
Non-probability Sampling
Non-probability sampling involves soliciting responses from a stream of people that differs from the true population. There is no known probability of selection. There are some people with zero probability of responding, and generally there are also some people who respond with certainty (i.e., 'professional' survey takers).