The fare basis code (often just referred to as a fare basis) is an alphabetic or alpha-numeric code used by airlines to identify a fare type and allow airline staff and travel agents to find the rules applicable to that fare.
A fare bucket is a group of fares within the same class. They are managed by the airline inventory system that opens or closes fare buckets according to the rules set by an airline as part of its revenue management strategy. That approach is called dynamic pricing and involves constant fare rate fluctuation depending on market conditions.
A Fare Bundle is a product that combines a Fare (right to fly) with additional ancillary products (lounge access, extra bags, wifi, etc). These bundles are typically discounted or given more favourable conditions than if purchased separately. In this way a customer can be attracted to spend more money where they otherwise may not have.
The rules and conditions by which the passenger(s) must abide by when flying with a fare product. These can be conditions such as penalties for refunding a restricted fare, or the amount of checked baggage available free of charge with your fare.