Is an oscillation the same as a period? Is one oscillation from peak to trough to peak again or is it just peak to trough? Doing a homework question and want to be sure I have the right definition
 A: 
Is one oscillation from peak to trough to peak again or is it just peak to trough?

This is a definition issue.
An internet search through some of the free dictionaries out there gives (link):

Physics.
a.  an effect expressible as a quantity that repeatedly and regularly fluctuates above and below some mean value, as the pressure of a sound wave or the voltage of an alternating current.
b. a single fluctuation between maximum and minimum values in such an effect.

And (link):

1. (General Physics) physics statistics
a. regular fluctuation in value, position, or state about a mean value, such as the variation in an alternating current or the regular swinging of a pendulum.
b. a single cycle of such a fluctuation

It has two meanings in physics: "an oscillation" can mean the very act that something is "swinging" in general. But about the other meaning, it seems the two sources do not entirely agree if "an oscillation" is between maximum and minimum or if it is a single cycle (that is, from maximum to maximum).
We are close to the answer, but a proper place for such a question would rather be https://english.stackexchange.com/


Is an oscillation the same as a period?

Your title is another question. And the answer is no.
The word "period" means something very specific, and is not the same thing as an oscillation in either meaning. A "period" is not the act of swinging, but the time for a complete cycle of the oscillation (from maximum to maximum). Usually denoted $T$ with units of seconds (or seconds per cycle if you like). 
A: Honoring the complex alternatives, here is a simple one: I would say, oscillation means a period of a periodical system in time.
