In general, Screening test is used to detect any speculated patients from healthy-looking subjects. These tests are used to pick up the speculated subjects from any subjects who have a high risk of the target disease (e.g. breast cancer) according to their personal histories. The screening tests usually have a high sensitivity but maybe can give false-positive result
After screening, the diagnosis will confirmed by using the combination of several techniques which have a high specificity and low false-positive as well as false-negative result.
Thus, they are difference in purpose and accuracy.
Early detection and screening are used for efforts to find asymptomatic disease, or at least disease that is not coming to the attention of a physician without the effort.
Screening refers to the effort made in all asymptomatic people, some of whom will be detected to have the disease.
When speaking about screening efforts, the term diagnosis is often used for disease that is surfacing outside of the screening efforts, e.g. symptomatically.
The term diagnosis is also used in the screening process where e.g. the screening test can be positive, which leads to referral for a more definitive test (or set of tests) which is then called diagnosis.
Outside of a screening discussion, the term diagnosis is used for any procedure to determine whether a person has a disease.