Is it different to say "they are coming to visit" from just "they are coming"?
Yes, the connotation is slightly different. We usually use "coming for a visit" to indicate that there is a purpose for the visit, such as meeting friends, family, conducting business, and so on. The verb "to come" is more simple and only includes the definition of moving or going closer to something. Thus, we usually use "come for a visit" or "visiting" to describe the act of calling upon others. Ex: I invited my friends to come for a visit this weekend. They have never visited my city before. Ex: I'm coming into work late because there was a lot of traffic.