There are several definitions for "case". It is often considered a synonym of "lawsuit", but for legal research "case" usually means the written decision/opinion of a judge or group of judges. These written decisions serve as authority or 'precedent', which is often binding and always important to subsequent decisions. The courts whose decisions are published are almost always appellate courts, not trial courts.
Many lawsuits will not have a written decision available either in print or on the web; the record will only be available at the courthouse in which the legal proceedings were held. For more information on how the law works see Legal Research: How to Find and Understand the Law (O"Neill Stacks KF 240 .E35 2015).