The ticketing system in Paris is quite complicated, but I'll try to explain it the best I can if someone needs to travel there some day.
As said previously, all of this is decided by IDFM (Île-de-France Mobilités), the Paris / Île-de-France equivalent of Transport for London, the RATP and SNCF have no say in the ticketing system and pricing.
CDG Airport is counted as a regular station in zone 5 for those wondering which tickets include it or not.
The most basic type of ticket is the T+ paper ticket (1.90€), it works for the Metro, RER, Trams and Buses. It doesn't work on the Transilien (suburban trains) network.
It works on the entire Metro network, and on the RER network only inside Paris (zone 1), in zone 1 you can transfer between RER and Metro freely using the same ticket you used to enter the system.
You can also use this type of ticket on trams and buses in the whole Île-de-France region (meaning all 5 zones, except T11 line which uses Transilien fares), and you can transfer freely between buses, trams and / or both for 90min. (You're not allowed to use the same ticket to do a round trip even within the 90min period)
There is no transfer included with the RER or the Metro, so if you need to take the bus and then the Metro you need 2 tickets.
You can have some weird situations outside of Paris, like in La Defense station where you can use this type of ticket to take the Metro between there and central Paris, but not the RER on the exact same route as La Defense is in zone 2.
If you need to travel by train outside of Paris (zone 1), you can buy paper tickets that will only be valid between the origin station and the destination station written on the ticket. If the origin or the destination is inside Paris and the other end of your journey is on an RER line, a T+ Metro ticket is included in the ticket.
Both these ticket types can be bought in a carnet of 10 tickets that will be slighty cheaper than bought individually.
You have also the Mobilis ticket for unlimited trips for 1 day, with prices ranging form 7.50€ to 18€ depending on the amount of zones. These work on all systems and all lines in the zones included in you ticket. It's essentially the same as a 1 day Travelcard in London.
There is a half priced version of the Mobilis for people that are 26 years old or less that is valid only on weekends (Ticket jeunes week-end).
This is the Paris version of the Oyster card, but less flexible than the latter.
I don't understand why they've made 2 versions of the same card with different fares, but whatever...
There is the Navigo Easy, essentially it's the paperless version of the T+ ticket. You buy a certain amount of virtual tickets that will be loaded to your card, and with each trip you'll use one of the virtual tickets.
The card itself costs 2€.
It is also possible to load this card with a 1 day Mobilis ticket or the half-priced version for young people.
The other version is the Navigo Decouverte. The card itself costs 5€ and you need an ID / passport photo that will have to be glued on your card (Yes this is important and the ticket inspector can charge you a fine if the photo is missing ...). On this card you can load the weekly or monthly fares. They abolished the zoning system for these so you can travel on any system anywhere in the whole Île-de-France region.
These are quite cheap (23€ for the weekly version and 75€ for the monthly one).
Of course there is a catch, you can't take these for any 7 days or 30 days time period. The weekly version must be from Monday morning until Sunday midnight, and the monthly version from the 1st day of the month to the 30th or 31st.
I don't recommend using paper tickets, it's complicated to know what you can or can't do and ticket inspectors won't care if you're a foreigner or not to fine you. If you will be travelling only inside Paris, take a Navigo Easy, and if you want to travel outside of Paris or will be staying for longer than 2-3 days, take a Navigo Découverte with a weekly or monthly fare.
If you take one of the fares that gives you access to all zones, you can visit the French countryside (a large part of zone 5 can be considered rural) and even travel on the last diesel operated passenger line in the Île-de-France region that goes from Paris-Est to Provins (It will be soon electrified).
I myself don't recommend the Paris Visite ticket, but if you plan to go some to the places that have price reductions associated with this ticket, it could be a good deal.
Oh and the Orlyval is not included in any of these tickets.