As soon as possible
This is the default constraint type. When you create a project, all tasks are scheduled to start on the same date as the project start date. To specify different start dates for the elements, you must define dependencies between project tasks, or manually change the start dates to later than the project start date.
For a project task that is not dependent on any other task, that is, a task with no predecessor, the task start date is the same as the project start date. With this default constraint, you can change the task start date to a later date, that is, a date later than the project start date.
For a task that is dependent on some other task, that is, a task with one or more predecessors, the task start date is the next working day after the finish date of all its predecessor tasks.
The constraint date is not available for this constraint.
Finish no later than
When you apply this constraint to a task, you must specify the constraint date, that is the date by which the task must complete.
For a task with this constraint, you can specify a proposed finish date that is the same as or earlier than the constraint date.
When you apply constraints to a task with dependencies, if the constraint affects the schedule constraint of a dependent task, you can either keep the dependency and remove the constraint, or remove the dependency and apply the constraint.