How to make thick and fluffy pancakes?
Separating the eggs and whipping the egg whites before folding into the batter could assist in this.  At home it's not a problem, but if it's a very busy that you had them in they're not likely to be doing this due to the fact that this will need to be done in batches. 

Adding a bit of baking soda in addition to the baking powder could assist as well, but only if you're using buttermilk.  If you're using regular milk the baking soda is going to create a soapy taste. In the case of buttermilk and baking soda, the primary leavening would be coming from the baking powder and then the acidity of the buttermilk would provide the reaction for the soda to give that extra "oomph".  If you're using baking soda then you'll have to use the batter right away otherwise those bubble will rise to the surface and pop, releasing their CO2 to the air. Same goes with adding seltzer water...add just before cooking the pancakes.

As for replacing milk with seltzer water...this will add bubbles to the batter but having less fat in the batter (presuming you're using whole milk) will increase the gluten development.  If you're using low-fat or nonfat buttermilk or regular milk it may not be as much of a difference.  The benefit of buttermilk (besides flavor) is the acidity that it provides.  Acidic doughs don't allow gluten to develop as easily and therefore create a more tender texture.

Overmixing pancake batter is a MAJOR issue with most people.  Make a well in the center of the dry ingredients, add the liquid ingredients which have already been beaten together and then carefuly fold just until combined so there aren't major pockets of dry ingredients but by no means should the batter be smooth.  Mixing to a smooth consistency will develop gluten and create tough pancakes.  A few lumps are fine as they will hydrate upon sitting.

If you're not using baking soda and seltzer water you can improve tenderness by letting your pancake batter sit after mixing for 30-60 minutes.  This is the idea behind chilling pastry crusts.  It not only allows gluten to relax but mainly it allows the starch granules of the flour to absorb moisture, hydrate, and expand (bloom).  This is could likely be part of what contributed to the pancakes you enjoyed at the restaurant.  If it's a very busy place, most likely they produce their pancake batter in large batches a day ahead for the next day's service.  This extended resting time would allow for maximum hydration of the starch which will make a thicker batter.  The thicker the batter the less spread you'll have on the griddle.  Obviously this provides limitations if you wake up with an appetite for pancakes!