The Paleo Diet - sometimes referred to as the Caveman Diet or the Paleolithic Diet involves eating mainly meats, seafood, vegetables, fruits, seeds and nuts.
The Primal Diet is very similar to the Paleo diet. It also involves eating mainly meats, seafood, vegetables, fruits, and nuts but also incorporates more healthy fats and allows for some legumes, beans and dairy.
More information on eating Primal can be found on Mark Sisson's Website: marksdailyapple.com
The Eat Clean / Clean Eating Diet is similar to the Real Foods Movement. It involves eating only real, whole foods. It is different from the Paleo and Primal Diets in that it allows grains & sugars among other things but the premise is good and is an excellent place to start if you aren't ready to go Full Paleo.
More information on following the Eat Clean diet can be found on Tosca Reno's Website: eatcleandiet.com
Many people have sensitivities to gluten and there are those that have Celiac Disease who can't tolerate even a little gluten and so they follow a Gluten Free Diet. Gluten Free is very popular right now but please remember... Gluten Free does not always mean healthy. You MUST read the nutritional labels!! If you can't pronounce the ingredients - i.e. the chemicals, preservatives, etc that they have put in those Gluten Free cookies, bread, etc.... then they aren't good for you!
Both the Paleo Diet and the Primal Diet are typically Gluten Free by default as neither diet allows grains.
More information on following the Gluten Free Diet can be found on the Celiac's Website: celiac.ca
There are many Whole Life Diet Programs. They all revolve around eating similar to Paleo, Primal and Eat Clean Diets but also incorporating wellness as a lifestyle.