****Update 3/1/2016: Merriam-Webster defines a vagrant as a person who has no place to live and no job and who asks people for money (in other words, a homeless begger). The word "vagrant" joins "transient" as a clue to the point of view of the communicator. Unless you know that the person is homeless, does not have a job, and begs for a living, calling them a "vagrant" demonstrates a lack of empathy for the plight of the homeless.
It is interesting to note that I recently read that it is not "politically correct" to say anything negative about a homeless person. This is a "new one" to me, but okay, I'll play: there are "good" homeless people and "bad" homeless people, just like everything else (good Catholic Priests vs. bad Catholic Priests; good lawyers vs. bad lawyers, etc.). I see no problem with factual statements about homeless people that are negative. However, generalizing about the homeless as bums, transients and vagrants without knowing anything about them is prejudicial and just wrong.
*****Original Article 12/25/2015: You can read more about the difference between a Homeless Person and a Transient person by clicking here. The article was written by a transient who does not consider himself to be homeless.
Let's make a few distinctions here: HOMELESS vs. TRANSIENT. A homeless person is someone who was previously housed, and through undesirable circumstances, they have become homeless. A homeless person may have their issues, like everybody else, but they want to get back into housing. Note that many homeless people in SLO county work full or part time, and still cannot afford our expensive local housing.
The HOMELESS most often feel shame for being homeless, and certainly do not advertise their state of affairs by panhandling or standing on a street corner waving one of those cardboard signs. They would sooner die of shame than work a corner asking for a handout, or aggressively panhandle spare change.
On the other hand, a TRANSIENT is someone who has chosen the homeless lifestyle. More often than not, when you meet them, they tell you they are just passing through, although it is also true that many have chosen to stay in one place for an extended period of time. Though it is true that a TRANSIENT may technically be HOMELESS, they themselves do not consider themselves to be homeless, but simply don't have a permanent address.
In general, TRANSIENT and VAGRANT terms are more pejorative term when compared with HOMELESS PERSON. In fact, one of the signs that a person or group has a negative point of view towards the homeless is when they refer to ALL homeless people as TRANSIENTS, or my other favorite, VAGRANTS. Another favorite of the "hate the homeless crowd" is simply BUMS. Our San Luis Obispo Police Department loves to refer to our homeless population as TRANSIENTS, thus tipping their hand to how they feel about them. Check out this link to this youtube video of SLO Police Chief Gessell where he talks about how they are dealing with the TRANSIENTS. The commentator in the youtube video interview uses the term TRANSIENT as well. Police are considered community leaders, and when they use the pejorative term TRANSIENT then others feel they can use them as well.