I tried some honey I got at a farmer's market and noticed it was really thick compared to regular honey you buy at any supermarket.
The raw honey at your farmer's market is likely unfiltered.
Usually raw, unfiltered raw honey can only be purchased directly from the bee farm. Characterised by fine textured crystals, it looks cloudier and contains particles and flecks made of bee pollen, honeycomb bits, propolis, and even broken bee wing fragments. Raw and unfiltered honey and has a high antioxidant level and will usually granulate and crystallize to a thick consistency after a few months. It is usually preferred as a spread on bread and waffles, or dissolved in hot coffee or tea. However, as most consumers are naturally attracted to buying and eating crystal clear and clean honey, unfiltered honey which looks cloudy and unappealing, is not commercially available on supermarket shelves.
Additionally, the pasteurization process helps keep the honey more liquid:
A lot of honey found in the supermarket is not raw honey but "commercial" regular honey, some of which has been pasteurized (heated at 70 degrees Celsius or more, followed by rapid cooling) for easy filtering and bottling so that it looks cleaner and smoother, more appealing on the shelf, and easier to handle and package. ... Heating also slows down the speed of crystallization in liquid honey. ... you may also find raw honey that are unprocessed but slightly warmed to retard granulation for a short period of time and allow light straining and packing into containers for sale.
This should be a comment but I am not yet able to do so.
My neighbour is a beekeeper and I asked him the same thing yesterday. The reason why (or rather when) honey crystallises or not is because of the ratio of glucose to fructose. The former tends to crystallise, the latter not so much, but in general every honey crystallises when left alone. Now as Chris already said, most commercial honey is heated to keep it fluid and more appealing (to some).
Acacia honey for example stays fluid for long periods of time even without heating, because of the high fructose content (but you can't really tell bees where to go, so no honey, whether from this or that flower, is 'pure').
There is also a honey that's really creamy, with a texture similar to Nutella. This is the result of stirring the honey continuously during the crystallisation process. This breaks up the bigger crystals into smaller ones which are submerged in the liquid part. Stirring also creates tiny air bubbles further contributing to the creamy texture.
Everything I wrote is only true for raw, unheated honey. I have no idea how creamy honey is made commercially, or how the productions differs.
In many countries, honey is usually labelled as "pure honey" and should not be adulterated with water or any other additive. Honey is expensive, so the honey companies use a nasty little trick to cheat a few cents from the unsuspecting buyer. When bees collect nectar, it is thinner than honey. They dump this nectar from their stomachs into honey cells and a row of bees at the bottom of the hive fan their wings to ventilate the hive. This dries the nectar, making it thicker and when it is thick enough, it becomes honey and the bees seal over the cell. Of course, its volume reduces when this happens as water is lost to evaporation. A small scale or craft beekeper will only take a frame of honeycomb out of the hive when it is ready, uncap the cells with a special knife and collect the nice thick honey. In commercial honey farms, they don't usually do this, instead, they don't wait for the honey cells to be capped off but they take out the honeycomb before the honey is properly thicked and extract it in a centrifugal machine before returning the empty combs to the hive. This way, the companies can squeeze a little more honey from each hive as it hasn't reduced volume so much during the ventilation process in the hive as much as proper honey. The customer gets a more runny and inferior product. It is theoretically possible that an unscrupulous producer may break product description law by adding water to the product to bulk it up, as this sort of adulteration is very hard to disprove - honey is partly water after all. Filtration removes bits of dead bee and wax from the honey but does nothing to change the thickness.
Commercial honey is frequently adulterated. It's not the same consistency because it's not pure honey.