Are the terms "event" and "outcome" synonymous?
Outcome and event are not synonymous.
Yes, an outcome is the result of a random experiment, like a rolling a die has six possible outcomes (say). However, an "event" is a set of outcomes to which a probability is assigned. One possible event is "rolling a number less than 3". See the Wikipedia page for probability theory and probability space for better descriptions.
I would say that an outcome is an elementary event (atomic event or simple event). A set of outcomes or elementary events is an event.
I would like to cite a section from the Wikipedia article on Outcome, which I think well summarises the relation between these terms
Since individual outcomes may be of little practical interest, or because there may be prohibitively (even infinitely) many of them, outcomes are grouped into sets of outcomes that satisfy some condition, which are called "events". The collection of all such events is a sigma-algebra.
An event containing exactly one outcome is called an elementary event. The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events.
Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite (most notably when the outcome must be some real number). So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events.