Orthodox, recalcitrant and intermediate are categories which reflect a species' tolerance to desiccation as seeds, also known as seed storage behavior.
Most species' seeds are orthodox, that is, the seeds survive under low moisture conditions and viability can be maintained through dry storage.
Recalcitrant species have seeds which die quickly (weeks-months) under low moisture conditions. They have limited storability because of this and either need to be sown and germinate or need to be stored under high relative humidity and cold temperatures (or other special environmental conditions) to maintain viability.
Intermediate seeds tolerate some degree of drying, in between orthodox and recalcitrant categories.
Generally seeds are orthodox, but species from humid or wet habitats and many trees may be recalcitrant. If you work with recalcitrant species, you need to be aware of this and use the seeds quickly or maintain them in moist cool conditions to avoid seed loss to death.
Also in general, seeds from the same taxon will have the same storage behavior.
For more information you can search "seed storage behavior"
A summary is available here to start:
And Kew's Seed Information Database is a way to search for the storage behavior of a given taxon (Family, Genus, Species)