The Floriated Cross is a cross with arms terminating in representations of flower petals. The flower is typically a lily.
The Foliated Cross differs in that it is a cross adorned with leaves. The leaves are typically those from a vine.
Cross names follow very loose conventions; whether in a heraldry, a Christian context or in art. There are several names for such bio-crosses, including Fleury Cross, Fleurée, Fleurettée, Fleuronny, Fleuronnée, Floretty, Floriated, Flory, Flourished and Foliated Cross.
To complicate things further (as heraldry often does) the shape of the Fleury Cross is very similar to the Fleur-de-lis Cross and the Patonce Cross. All these names are used interchangeably and in most cases the distinction is not important. (The Patonce Cross differs in that its end spread outwards like a Pattee Cross whereas the Fleury Cross arms do not expand.)
Not only do the arm-ends represent flowers, but they also have the appearance of horns or crowns. (See also the similar Trident Cross.)
These crosses are used mainly in heraldry, especially in France. Fleury, with its many spelling variations, is the name given to the Côte Fleurie (Flowering Coast) in Normandy, northern France, with its bizarre tourist 'attraction' of the D-Day landing beaches.
In the Fleury Cross, as with the Fleur-de-lis and Patonce Crosses, the three petals represent faith, wisdom and chivalry when used in heraldry, and the Trinity when used as a Christian Cross.