I was just wondering if I was comprehending clocks in the correct way, so far this is what I understand.

So there is the clock generator which can either be a clock, a crystal oscillator, or a voltage-controlled crystal oscillator. That clock generator creates the clock signal or clock pulse (which I use interchangeably but I do understand that the pulse is the actual up and down whereas the signal is the transmission of energy carrying information). There are two pulses, one positive, one negative, and within each pulse there are two edges (also positive and negative). The measure of how long it takes for one positive or negative pulse to go back to another positive or negative pulse is known as the period (T). And the measure of how long it takes for one clock cycle to occur per second is known as the frequency (A clock cycle being one positive and one negative pulse occurring adjacently to each other) Now here's where I get confused. Are clock speed and frequency 2 different things? Because I have it here that the clock speed would be the number of pulses per second, but if it's the same as clock frequency, then my idea that it's the amount of cycles per second is wrong. Either that or clock speed is the same as period...

Someone recently told me that clock frequency = clock speed, and that it is just the reciprocal of the period (T) and isn't anything else.
Welcome to the CH forum.
You may be talking about the SYSTEM clock for the CU or the real time clock tact gives the hours and minutes, etc.
Quartz crystals are often USED as reliable fixed-frequency time reference.
A full discussion of Quartz oscillators would take a couple of pages. Let's just say that are in common use in many electronic devices. The accuracy and stability of quartz makes digital processing reliable. An oscillator running at 10,000,000 Hertz could run all day at near room temperature and not even drift 10 Hertz. Or put  another way, one part per million.
Digital dividers are used to scale down  the frequency by some integer divisor.. Also, other types of devices can multiply frequency up by integer multiple.
 The following is an article that gives a basic outline.
http://en.wikipedia.org/wiki/Crystal_oscillator
Quote

Quartz crystals are manufactured for frequencies from a few tens of kilohertz to hundreds of megahertz. More than two billion crystals are manufactured annually. Most are used for consumer devices such as wristwatches, clocks, radios, computers, and cellphones. Quartz crystals are also found inside test and measurement equipment, such as counters, signal generators, and oscilloscopes.

Someone recently told me that clock frequency = clock speed, and that it is just the reciprocal of the period (T) and isn't anything else.

The quartz crystal
Every motherboard will have at least one quartz crystal. This generates the basic timing signal that is used to produce the various frequencies required by the different parts of the system bus, as well as the processor speed itself. The crystal will usually be in the form of a small silver-colored can, about 1/8-inch high, mounted on the board with its top end visible. That end of the crystal will usually have a frequency printed on it, typically 14.318 MHZ (see Figure A).