Fluorescence is a relaxation process from a singlet excited state to a singlet ground state (requiring no change in electron spin of the demoted electron). Whereas, phosphorescence is a relaxation process from an excited triplet state to the ground singlet state, requiring a change in electron spin during an electronic state transition and thus making it a forbidden process (not strictly forbidden). Hence relaxation from a triplet excited state to ground electronic state will usually require more time than relaxation from a singlet excited state. However, with that stated you can have "delayed-fluorescence" which would be on the same time-scale as phosphorescence.
Because of "excange energy", the lowest lying triplet excited state will be of lower energy than the lowest lying singlet excited state. If we assume Kasha's rule holds (it doesn't always), than the emission resulting from phosphorescence will occur at lower energies than fluorescence.
Also, because lifetimes of triplet excited states are longer lived than singlet excited states, phosphorescence lifetimes will be shortened and phosphorescence intensity will be lowered to a greater extent by collisional quenching than that of fluorescence. So removing oxygen from the sample will have a significant impact on phosphorescence lifetimes and intensity.
Fluorescence is a relaxation process from a singlet excited state to a singlet ground state (requiring no change in electron spin of the demoted electron). Whereas, phosphorescence is a relaxation process from an excited triplet state to the ground singlet state, requiring a change in electron spin during an electronic state transition and thus making it a forbidden process (not strictly forbidden). Hence relaxation from a triplet excited state to ground electronic state will usually require more time than relaxation from a singlet excited state. However, with that stated you can have "delayed-fluorescence" which would be on the same time-scale as phosphorescence.
Because of "excange energy", the lowest lying triplet excited state will be of lower energy than the lowest lying singlet excited state. If we assume Kasha's rule holds (it doesn't always), than the emission resulting from phosphorescence will occur at lower energies than fluorescence.
Also, because lifetimes of triplet excited states are longer lived than singlet excited states, phosphorescence lifetimes will be shortened and phosphorescence intensity will be lowered to a greater extent by collisional quenching than that of fluorescence. So removing oxygen from the sample will have a significant impact on phosphorescence lifetimes and intensity.
ESR should immediately indicate whether your compound exhibits a measurable triplet excited state, indicative of phosphorescence. Alternatively, you can perform emission measurements in the presence of a selective triplet quencher (i.e. if there's no drop in luminescence intensity, you're observing fluorescence).
As mentioned in earlier answers, fluorescence is the transition from the first excited singlet state to the electronic ground state: S1 S0 (apart from a relative small number of exceptions, such as for azulene with S2 S0. Phosphorescence is the transition from the lowest triplet state (not an excited triplet state) to the singlet ground state: T1 S0. The spin reversal required for this process makes it a forbidden transition, leading to a long triplet lifetime, generally of the order of seconds., much longer than that of S1, with a lifetime of at most several hundreds nanoseconds (pyrene). The long lifetime of the triplet states makes it very sensitive to diffusional quenching, such as by oxygen. Therefore, phosphorescence can generally not be seen in fluid solution, but will only be observed in frozen (or at least solid) solution. The absolute proof that a luminescence appearing by freezing a solution is phosphorescence, is the observation of a triplet signal in an ESR experiment. The increase or decrease of luminescence intensity as a function of temperature is not a valid or useful criterium.
Briefly, you can test whether your compound is fluorescent or phosphorescent in such an experiment: prepare the solution for the measurement in oxygen-free conditions (if there is no glovebox available, then just seal the cuvette and buble with Ar for a few minutes) and measure the emission spectrum. Then open the solution to air, wait a little bit and register the emission again. If a significant decrease of the emission intensity, compared to the first spectrum, will be seen - the compound possesses phosphorescent properties.
Of cause, to confirm this your also need to measure emission lifetime.