Although many tests are referred to by a generic term like "intelligence" or "achievement," they may actually measure different facets of behavior. For example, some reading achievement instruments emphasize word recognition while others emphasize comprehension. Some intelligence tests are more verbally oriented than others. For example, when immigrants entering the U.S. through Ellis Island were assessed using a particular intelligence test, examiners found that those coming from English-speaking countries scored higher than those coming from non-English speaking countries. Surprise!
Similarly, group tests often give different results than individual tests. In an individual situation, the examiner can closely monitor a child's behavior to be sure she is following the test, to note particular problems with motor skills or anxiety, or to probe answers (where appropriate) to obtain more information.
Situational variables also affect test performance. If one gives a creativity test near a holiday and asks children to make pictures out of a series of circles, one will get more jack-o'-lanterns at Halloween, but more ornaments at Christmas. Illness, lack of sleep, or skipping breakfast can also impair performance. It is also not uncommon for test scores to change over the life of an individual, particularly if the initial assessment was done during the preschool years. Young children's test scores are less stable and more variable.
Finally, assessment measures should be designed to tap the abilities that will be important to success in the environment. Anecdotally, we often hear of individuals who did well on the SAT or ACT and got great grades in college who nevertheless didn't excel in their chosen profession. SATs and ACTs are good predictors of college grades, but success in life requires other abilities, including social skills such as getting along with co-workers.
With respect to your daughter's scores, I would recommend that you contact the school psychologist who serves your daughter's school. Make an appointment with him to discuss your daughter's various scores. Do provide the school psychologist with the test results from the various sources that assessed her. You can request that previous testing be sent to the psychologist in advance of your meeting. A school psychologist can explain the various tests (e.g., what they are designed to measure), discuss your daughter's performance, and comment on how that is relevant to her current performance.