From what I understand:
Cross - The method used to create a hybrid. 'Crossing' two strains means forcing sexual reproduction between two strains with different traits. I usually only consider the F1 variety to be a cross.
Hybrid - A strain created from two different parent strains
Interspecific hybrid - A strain created by crosses between two or more different species
Stability - How predictable the traits of a plants offspring will be. If the plant is very stable, the plant's traits will be very similar year after year. If it is unstable, two seeds planted from the same pod could produce two very different plants.
F1 - The FIRST generation of a hybrid strain. The seeds planted from the pod produced from a crossed flower produce F1 plants.
F2, F3, F4, etc - The subsequent generations of a hybrid strain. Flowers are either self-pollinated or pollinated by other flowers from the same plant. The number after F tells us which generation the plant is.
That's just how I've always looked at it. More definitions definitely welcome in case I'm mistaken.