What is the difference between the GUMMY BEAR breast implant and SILICONE memory gel implants?

Memory gel and gummy bear both refer to the same class of newer generation silicone gel breast implants.  They offer a stiffer version of gel that helps to keep the form of the implant, with less effect by gravity.  Memory gel is associated with a brand of implants (Mentor), while similar Allergan implants are called 410s.  There are slight differences in the firmness of the implants between the two brands, but are meant to perform the same role. "Gummy bear" is more of a generic term, as is "cohesive gel", and "form stable" implants.  The newest generation of silicone gel implants are much stiffer than those in use 30 years ago, and the implant shell (the outer material) is also thicker as well.  You can learn more about the difference during an in person consultation.  Please seek a plastic surgeon certified by The American Board of Plastic Surgery.

Cohesive gel?…Form stable?...Gummy Bear?…Memory Gel? What do these terms have in common? With the recent introduction and FDA approval of the next generation of devices, the attention of patients, physicians and the media has been focused on these terms. While these devices have certainly captured the public’s attention, an in-depth understanding continues to evade most.
Following the FDA moratorium on the use of silicone gel filled breast in 1992, “cohesive gel implants” were introduced to the market. How do these devices differ from their predecessors? The silicone gel of a cohesive gel implant is firmer (via the addition of proprietary cross-linker). The greater the cross-linking the firmer the device will feel. The result is a filling that doesn’t leak when the shell is compromised in the way that a traditional liquid does. This quality is best illustrated when cutting a device in half…it doesn’t yield a gooey mess but instead two stable halves.

Generally speaking today’s silicone implants are all “cohesive gel implants” to some extent.This broad term has been inappropriately applied to the next generation of “highly cohesive gel implants.” However, the recent media attention on “cohesive gel implants” is not warranted and is in fact misplaced.

These newest devices to reach the market are form stable implants.  These higher strength silicone gel implants were approved by the FDA in March 2012. They contain a more “highly cohesive gel.” This increase confers upon these devices the ability to maintain shape irrespective of position. This quality has earned them the informal nickname of “Gummy Bear” implants. Imagine cutting into a gummy bear candy and the effect is the same.

While these implants are new, “novelty” does not necessarily equal “better.” There is a device for every patient. Form stable implants have both advantages/disadvantages. The advantages are: shape retention, no shell folding/wrinkling, no leakage, decreased capsular contracture. The disadvantages include: increased cost, limitations related to access incision, increased technical difficulty, and potential for device rotation. Additionally, the texturing which has been employed to address potential device rotation has now been associated with BIA-ALCL.
There are currently 3 devices with FDA approval available to the public at large which fall into what could be broadly described as the "Gummy Bear" category. They are the Allergan/Inamed 410, Mentor Memory Shape, Sientra. Each represents a different point along the cohesive gel spectrum, the former being the firmest and the latter the softest.
With regards to your specific question, MemoryGel is a term Mentor has coined for their cohesive gel implants. As I described above "Gummy Bear" is a term which has been loosely applied to a number of different devices but most accurately describes the form stable devices (highly cohesive). 
In general, traditional round silicone implants are preferred over saline implants by many patients and surgeons for their more natural feel. These devices are also more commonly employed in the cosmetic setting relative to the form stable devices. However, as you can see from the offerings described above, there are a myriad of options available to patients.Patients are encouraged to have an in-depth consultation with their board certified plastic surgeon before selecting a particular type of implant. While form stable anatomic implants are newer, they may not be suitable for all patients. 

Hello, "gummy bear" means different things to different people.  Some people use this term to describe teardrop-shaped silicone gel implants, but others use this term to describe any silicone gel implant (round or teardrop) with highly cohesive thick gel inside.