Pilot (Test, Project, Study)
This could be basic (pure) research or applied research of any kind--survey, experiment, ethnographic field work.

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Replication Research
1. This could be an effort to duplicate pilot research to see if a phenomenon (e.g., results of a survey or experiment, generalizations from ethnographic research) are reliable (repeatable).

2. This could also involve a modification of pilot research to assess the generalizability of findings; e.g., to a sample with different characteristics, or to the same kind of sample but in a different environment (e.g., a different experimentally designed intervention with the same sort of participants, or an ethnographic study of methods by which inmates "make do" not only in mental hospitals but also in nursing homes).

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Demonstration Project
This could be a larger scale study--more variables; more instruments; different kinds of instruments (questionnaires and interview schedules and direct observation and documents) to measure the same and different variables; more control if an experiment; and/or a sample that is more representative of the population to which the findings may generalize. Usually, this is applied research.

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Dissemination Research.
This has many of the same features of replication research. Are the outcomes of a demonstration project (e.g., of an intervention) found when the intervention is used in another community? If not, how might the intervention be modified? Usually, this is applied research.

Note that both demonstration and dissemination research would have large components of evaluation research. For example, one would be asking: 1) What was done? 2) What were the outcomes in relation to the objectives? 3) What were the problems in implementation and in outcomes (anticipated and unanticipated)? 4) What were the benefits in relation to investments and costs--and in comparison (if possible) to other interventions?