The difference between the sample result and the result of an accurate census is called:

I think they key is in Peter Ellis' answer: "attempted". When you do sampling properly, you sweat the details of non-response, figure out strata and seek them out, etc. When you decide to do a census, it's easy to ignore those issues, since you're getting "everyone". Problem is, you're probably not getting everyone, but you're not thinking about who you're not actually getting.

There are also statistical issues with extremely large samples (as a proportion of the sampled population). I'm not sophisticated enough to understand them, but at a minimum you have problems with variance calculations. (Packages like R's survey compensate for such things in large subpopulations of a survey, and that's where I first learned about this.)

As a secondary issue, if non-sample error includes issues due to quality control at various steps in the process, having enormously more data (census) would make it much harder to have the level of quality control that you would have (with the same resources) on a smaller set of data (sample).

Imagine if you had the resources (financial and personnel) that the US Census Bureau used for a census, but you were only doing a survey of 1,000 random adults. I think you'd have much better quality control and much better analysis of the issues involved and of the data itself.

How do we study a population?
A population may be studied using one of two approaches: taking a census, or selecting a sample.

It is important to note that whether a census or a sample is used, both provide information that can be used to draw conclusions about the whole population.

What is a census (complete enumeration)?
A census is a study of every unit, everyone or everything, in a population. It is known as a complete enumeration, which means a complete count.

What is a sample (partial enumeration)?
A sample is a subset of units in a population, selected to represent all units in a population of interest. It is a partial enumeration because it is a count from part of the population.

Information from the sampled units is used to estimate the characteristics for the entire population of interest.

When to use a census or a sample?
Once a population has been identified a decision needs to be made about whether taking a census or selecting a sample will be the more suitable option. There areadvantages and disadvantages to using a census or sample to study a population:

How are samples selected?

A sample must be robust in its design and large enough to provide a reliable representation of the whole population. Aspects to be considered when designing a sample include the level of accuracy required, cost, and the timing. Sampling can be random or non-random.

In a random (or probability) sample each unit in the population has a chance of being selected, and this probability can be accurately determined.

Probability or random sampling includes, but is not limited to, simple random sampling, systematic sampling, and stratified sampling. Random sampling makes it possible to produce population estimates from the data obtained from the units included in the sample.

Simple random sample:

All members of the sample are chosen at random and have the same chance of being in the sample. A lottery draw is a good example of simple random sampling where the numbers are randomly generated from a defined range of numbers (i.e. 1 through to 45) with each number having an equal chance of being selected.

Systematic random sample:

The first member of the sample is chosen at random then the other members of the sample are taken at intervals (i.e. every 4th unit).

Stratified random sample:

Relevant subgroups from within the population are identified and random samples are selected from within each strata.

In a non-random (or non-probability) sample some units of the population have no chance of selection, the selection is non-random, or the probability of their selection can not be determined.

In this method the sampling error cannot be estimated, making it difficult to infer population estimates from the sample. Non-random sampling includes convenience sampling, purposive sampling, quota sampling, and volunteer sampling

Convenience sampling: Units are chosen based on their ease of access;

Purposive sampling: The sample is chosen based on what the researcher thinks is appropriate for the study;

Quota sampling: The researcher can select units as they choose, as long as they reach a defined quota; and

Volunteer sampling: participants volunteer to be a part of the survey (a common method used for internet based opinion surveys where there is no control over how many or who votes).

Collecting data about a population flowchart:

Collecting Data about a Population Flowchart: Census and Sample

Recommended: Read Data Sources next

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Further information:
ABS:
1299.0 - An Introduction to Sample Surveys: A User's Guide
Sample Size calculator

External links:

Basic Survey Design: Samples and Censuses

What is the difference between a census and a study that is not a census?

What is meant by sampling error?

Which type of error occurs when certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame?

When a researcher has made the decision to obtain a sample the first step in the selection of the sample is to?