On most systems, a light-weight process also differs from a full-blown process, in that it only consists of the bare minimum execution context and accounting information that is needed by the scheduler, hence the term light-weight. Generally, a process refers to an instance of a program, while an LWP represents a thread of execution of a program (indeed, LWPs can be conveniently used to implement threads, if the underlying kernel does not directly support them). Since a thread of execution does not need as much state information as a process, a light-weight process does not carry such information.
As a consequence of the fact that LWPs share most of their resources with other LWPs, they are unsuitable for certain applications, where multiple full-blown processes are needed, e.g. to avoid memory leaks (a process can be replaced by another one) or to achieve privilege separation (processes can run under other credentials and have other permissions). Using multiple processes also allows the application to more easily survive if a process of the pool crashes or is exploited.