The mob in front of the Finch’s house is mostly people Atticus is friends with. They are asking Atticus why he took Tom’s case and they also think moving Tom to the county jail will cause trouble. It turns out they are correct. A mob mostly of strangers, including Walter Cunningham, show up most likely to capture Tom and kill him.
Atticus is well aware that a mob thinks differently from individual people. In each case, he remains calm and logical. In each case, he asks “Do you really think so?” As Scout mentions, this is a sign that Atticus is going to act and a sign that he has the upper hand. Atticus also uses this phrase to single a person out and, in a glimmer of hope, to get that person to think logically.
The mob in front of the Finch’s house is less threatening but they still think like a mob. The reader gets the impression that Atticus will handle the situation in his normal logical way. But Jem and Scout break up both mobs. Jem breaks up the first mob with distraction. By defying Atticus outside the jail, he initiates the breakup of the mob. Scout completes it by singling out Walter Cunningham and making polite conversation. Here we see the innocence and bravery of children in the face of the ignorance and cowardice of a thoughtless mob.
Atticus didn't want the children involved for their own safety. But on the walk home, it is clear that he is proud of them.
Interestingly, it appears that Harper Lee intends for the reader to make this observation of the similarities and differences between the two groups of men. For, the men of one group appear in the front yard of the Finch home after supper in Chapter 15 as a preface to the others' appearing at the jail in Chapter 16 of To Kill a Mockingbird.
Among the men who call Atticus outside from his house in Chapter 15 are Sherriff Heck Tate and Mr. Link Deas, who owns the newspaper. They are concerned about Tom Robinson's being put up in the jail the next day, and want a change of venue for the trial. But, Atticus thinks that they are overly concerned, "Don't be foolish, Heck....This is Maycomb." Nevertheless, Mr. Deas says that he is worried about "that Old Sarum bunch" who "get liquored up." Atticus argues that they do not usually drink on Sundays, and he holds to his conviction that Tom deserves a fair trial. There is a murmur of discontent and the men move closer to Atticus. However, when the phone rings, Jem shouts to his father and Atticus tells him to answer it, laughter breaks up the crowd composed of people that the Finches observe every day: merchants, in-town farmers, Dr. Reynolds, and even Mr. Avery.
On the following evening at the jail, though, it is a much different crowd that Scout and Jem, who follow Atticus out of concern for him, observe. These men have their collars pulled up and hats dragged down over their ears so they will be indistinguishable from one another. Scout remarks that there is "a smell of stale whiskey and pigpen" in the air, and when she looks around, she realizes the men are strangers to her:
They were sullen, sleepy-eyed men who seemed unused to late hours.
When Scout finally recognizes Mr. Cunningham, he looks away as she speaks. This crowd of men do not wish to be individualized as were Mr. Tate and Mr. Deas. Forming a semi-circle around Atticus, they become a mob, possibly equipped with weapons since they have on more clothes than necessary for the weather. But, again the children mitigate the tension as this time Scout speaks to Mr. Cunningham. As he is singled out, Mr. Cunningham becomes uncomfortable and no longer wishes to threaten Atticus Finch, who has always treated him fairly. So, he motions to the others to go, and they follow his lead. This action also is in contrast to the other men at the Finch home, who each laugh and disperse of his own will.