What is the difference between being affiliated and being associated with a group of people?
Affiliation is generally a closer and more formal connection than association is. I think affiliation is used more in the professional world than outside. There is a connotation of exclusivity with affiliation. If someone is affiliated with, say, one university, he or she is probably not affiliated with other schools.
(Also, regarding preposition choice, note that in the U.S. you would usually say or write that you are affiliated with or associated with a group of people.)
Absent any context, affiliated connotes a formal relationship, such as membership, partnership, ownership, or other contractual connection. While associated can also carry this meaning, it can also be used to describe more casual connections, or even where the connection is made only by outsiders.
Context is very important, however, as narrower meanings may apply in various industries, organizations, or legal realms. An "affiliated person" in a U.S. trust or thrift for example, is a person with direct influence in the affairs of the organization, such as an officer or owner (or spouse or immediate family member thereof); "associated person," on the other hand is not to my knowledge assigned any special definition.
An organization might use both terms and define "affiliation" as stronger than "association" or vice versa. It might not use them to express a degree of affiliation at all, however; perhaps "affiliated" refers to members, "associated" to their spouses. There is very little consistency even among organizations of the same type, such as universities or sports federations.
Affiliated is a relationship of dependancy, and usually the referent is an organisation rather than an individual. An affiliated school,for example, would operate independently but collaborate with a larger institution that has influence over the schools standards, programmes, exams, etc.
Associated is a relationship of shared purpose or values. The Football Association is for footballers, who presumably all have a shared purpose in promoting football.
You have a core group of network, then you have various member groups. Then affiliated non-member groups, who use the network resources but are not controlled members of the network's core group. These affiliated groups operate within the network but are not member groups. Then you have the pro-network, non-network allied groups or networks, who are friendly to the network. Then you have breakaway groups, who were created by/originated from the network core group, as a member group various but broke away or exited the network. Finally, you have the unstable, pro-network groups or individuals, who are the "loose cannons" or "wild cards", who believe in the network but are not officially organized or only organized in special situations, to commit crazy brutal acts, demonstrations, rallies, meetings, etc. all of these types of connections form a group's association to a network, usually.