What does it mean for a country to be a FIDE "Affiliated Organization" instead of a FIDE Member? According to the latest FIDE newsletter the Isle of Man has become a FIDE affiliated organization:

The General Assembly approved the admission of the Isle of Man Chess Association as an affiliated organization. This is in recognition of the Isle’s continued contribution to chess, including what promises to be one of the world’s major chess events next year, the FIDE Chess.com Grand Swiss. The vote saw 107 votes in favor and just 4 against, with a further 4 abstentions.
The status of “Affiliated Organization” is slightly below that of full “Member Organization”, which according to Article 9.4 of the FIDE Charter, would demand a territory to be recognized by the United Nations and the International Olympic Committee.

According to the FIDE directory of affiliated associations these are either continental or linguistic groups of countries like the Portuguese-Speaking Federations Association, the European Chess Union, the African Chess Federation, the Chess Association of Black Sea Countries, the Confederation for Chess for Americas, or related chess associations which have nothing to do with countries like the International Correspondence Chess Association, the International Computer Games Association, the International Physically Disabled Chess Association, the World Federation for Chess Composition.
Member federations are normally countries although many of them do not satisfy the criteria of being members of the IOC or United Nations. So, for instance the UK has a seat at the UN and is an IOC member but there is no single UK FIDE member. Instead there are separate England, Scotland and Wales members and there is even one member which crosses borders, the Ireland member which includes the country of Ireland AND Northern Ireland which is part of the UK.
The Isle of Man is a slightly strange country in that it is a Crown Protectorate like Jersey and Guernsey, both of which are FIDE members. It has its own parliament and government with tax raising powers but relies on the UK for defence.
It is also quite small with a population about 85,000. However even in Europe there are several FIDE member countries which are smaller - Andorra (72,000), Guernsey (65,000), Faroe Islands (50,000), Monaco (38,000), Liechtenstein (37,000), San Marino (33,000).
What does this change mean for Isle of Man chess players, who will continue to be England players as far as FIDE registration and representation is concerned?
It doesn't appear that this will have a large impact on the players themselves. The organization can organize events and gets nonvoting representation in FIDE.
According to the FIDE Charter:

14.1 The General Assembly, following an advisory opinion of the Council, can be admitted as Affiliated Organisations:
a) organisations grouping Member Federations;
b) associations or organisations which represent some regions or transnational territories;
c) associations or other organisations representing people with a common ground or with same interests on some specific chess activities.
14.2 Affiliated Organisations have the right to take part in FIDE Congresses and in the General Assembly, without voting.
14.3 Affiliated Organisations can organise and participate in some specific FIDE competitions or events, according with FIDE rules and regulations.
14.4 Affiliated Organisations can be authorised to organise events under the auspices of FIDE.
14.5 Affiliated Organisations can be temporarily suspended or permanently expelled by the General Assembly, for just cause.

As for why the situation with other UK protectorates is what it is, I suspect that these rules have something to do with it (emphasis mine):

9.2 Only one Federation for each country can be affiliated to FIDE as a Member. This rule shall not apply to Federations that were accepted as FIDE Members before the date of this Charter entering into force.


9.4 For new members, the country of the federation must be a country recognised by the United Nations and the International Olympic Committee(IOC).