Lamport logical clock: what does partial mean in the concept of `Partial ordering`?

Question

In lamport's paper[1], he define two concept The partial ordering and The totally ordering.

1. What does partial mean in partial ordering?

   assumption: this ordering only handle two cases, one is to order events happening in single process, second is communication events between two process. It can't handle concurrent events, so it's named as Partial ordering.

   Is my assumption correct?

2. What does totally ordering mean?

   Does that mean it can handle all the events in a distributed system?

Reference

Lamport, “Time, Clocks, and the Ordering of Events in a Distributed System.”