A similarity between Candy and his dog and George and Lennie lies in how people have companions despite a world where most are individualistic.
The world that Steinbeck creates is an individualistic one. Ranch hands move in and out of work settings on their own, like transients. They are on their own, solitary and isolated. People who are there today are not there tomorrow. This world speaks to the economic hardship that besieged many. People moved around the country to find work and did not really seek to forge emotional attachments in the name of subsistence.
In Chapter 3, George and Lennie and Candy and his dog are exceptions to this rule. Both sets of characters travel together. They are not isolated from others. Rather, they demonstrate a sense of community in a world that is highly atomized. George and Lennie buck the trend in how they travel together. They go from place to place, looking for work. However, they do so as a pair. In the same way, wherever Candy goes, so does his dog. They are inseparable. In a setting where there is little camaraderie, George and Lennie and Carlson and his dog challenge this prevailing trend.
George and Candy go out of their way to prove to others the merits of their companions. For example, when talking to the boss about Lennie, George says that while Lennie might not be smart, "he's sure a hell of a good worker. Strong as a bull." In the same way, when George remarks to Candy how old his dog is. Candy responds with a supportive advocacy for his companion: "Yeah. I had ‘im ever since he was a pup. God, he was a good sheepdog when he was younger." A similarity between George and Lennie and Candy and his dog is that the dominant companion in the relationship feels obliged to defend their counterpart to others.