I've been hearing people talk about Penitum and Celeron processors like they were completely different than i3,i5, and i7 processors. Could someone please tell me why this may be and how Pentium or Celeron performs compared to i3, i5, or i7.
Short answer: i3/i5/i7 CPUs are better at running multi-threaded applications.
For example the G3258 and the i3 are both dual core processors but the i3 can perform hyperthreading meaning each core can run two threads (giving the equivalent of 4 virtual cores).
There are currently two different lines of Celeron and Pentium CPUs. The 1st line is the more powerful version which is basically Core i3 CPU with reduced features like no hyper threading a less powerful Intel HD graphics core with no model number; it is simply called the "Intel HD" graphics core and can make things a bit confusing to many people. Current generation of desktop Celerons based on the Core i3 are called "Celeron J" and "Celeron G"; examples are the Celeron J1800 and Celeron G1840. Current generation of desktop Pentium CPUs based on the Core i3 CPU are called "Pentium G"; an example is the Pentium G3460.
In the laptop world things get a bit more complicated. Mobile Celeron and Pentium CPU based on the mobile version of the Core i3 are simply called "Celeron" and "Pentium" with a model number; examples are the Celeron 2918U and the Pentium 3560M. However, Intel has decided to move the Celeron and Pentium brand names into their inexpensive and less powerful line of mobile CPUs known as the Atom series CPUs.
While Atom CPUs may draw upon some design features of mobile Core i3 CPUs, these Atom CPUs are designed to draw little power and also cost much less to manufacture. They are targeted at tablets and low cost laptops. These Atom series Celeron and Pentium CPU are designated as "Celeron N" and "Pentium N"; examples are the Celeron N2940 and the Pentium N3540.