(FISP) A fast imaging sequence, which attempts to combine the signals observed separately in the FADE sequence, generally sensitive about magnetic susceptibility artifacts and imperfections in the gradient waveforms. Confusingly now often used to refer to a refocused FLASH type sequence.
This sequence is very similar to FLASH, except that the spoiler pulse is eliminated. As a result, any transverse magnetization still present at the time of the next RF pulse is incorporated into the steady state. FISP uses a RF pulse that alternates in sign. Because there is still some remaining transverse magnetization at the time of the RF pulse, a RF pulse of a degree flips the spins less than a degree from the longitudinal axis. With small flip angles, very little longitudinal magnetization is lost and the image contrast becomes almost independent of T1. Using a very short TE (with TR 20-50 ms, flip angle 30-45°) eliminates T2* effects, so that the images become proton density weighted. As the flip angle is increased, the contrast becomes increasingly dependent on T1 and T2*. It is in the domain of large flip angles and short TR that FISP exhibits vastly different contrast to FLASH type sequences. Used for T1 orthopedic imaging, 3D MPR, cardiography and angiography.

(PSIF) A heavily T2* weighted contrast enhanced gradient echo (mirrored FISP) technique. Because TE is relatively long, there are much flow artifacts and less signal to noise. In normal gradient echo techniques a FID-signal results after the RF pulses. This FID is rephased very fast and just before the next FID follows a spin echo signal. The SE is spoiled in FLASH sequences, but with PSIF sequences, only the SE is measured, not the FID.

Contrast enhanced GRE sequences provide T2 contrast but have a relatively poor SNR. Repetitive RF pulses with small flip angles together with appropriate gradient profiles lead to the superposition of two resonance signals.
The first signal is due to the free induction decay FID observed after the first and all ensuing RF excitations.
The second is a resonance signal obtained as a result of a spin echo generated by the second and all addicted RF-pulses.
Hence it is absent after the first excitation, it is a result of the free induction decay of the second to last RF-excitation and has a TE, which is almost 2TR. For this echo to occur the gradients have to be completely symmetrical relative to the half time between two RF-pulses, a condition that makes it difficult to integrate this pulse sequence into a multiple slice imaging technique. The second signal not only contains echo contributions from free induction decay, but obviously weakened by T2-decay. Since the echo is generated by a RF-pulse, it is truly T2 rather than T2* weighted. Correspondingly it is also less sensitive to susceptibility changes and field inhomogeneities.
Companies use different acronyms to describe certain techniques.
Different terms (see also acronyms) for these gradient echo pulse sequences:
CE-FAST Contrast Enhanced Fourier Acquired Steady State,
CE-FFE Contrast Enhanced Fast Field Echo,
CE-GRE Contrast Enhanced Gradient-Echo,
DE-FGR Driven Equilibrium FGR,
FADE FASE Acquisition Double Echo,
PSIF Reverse Fast Imaging with Steady State Precession,
SSFP Steady State Free Precession,
T2 FFE Contrast Enhanced Fast Field Echo (T2 weighted).
In this context, 'contrast enhanced' refers to the pulse sequence, it does not mean enhancement with a contrast agent.

(TrueFISP) True fast imaging with steady state precession is a coherent technique that uses a fully balanced gradient waveform. The image contrast with TrueFISP is determined by T2*//T1 properties and mostly depending on TR. The speed and relative motion insensitivity of acquisition help to make the technique reliable, even in patients who have difficulty with holding their breath.
Recent advances in gradient hardware have led to a decreased minimum TR. This combined with improved field shimming capabilities and signal to noise ratio, has allowed TrueFISP imaging to become practical for whole-body applications. There's mostly T2* weighting. With the used ultrashort TR-times T1 weighting is almost impossible. One such application is cardiac cine MR with high myocardium-blood contrast. Spatial and temporal resolution can be substantially improved with this technique, but contrast on the basis of the ratio of T2* to T1 is not sufficiently high in soft tissues. By providing T1 contrast, TrueFISP could then document the enhancement effects of T1 shortening contrast agents. These properties are useful for the anatomical delineation of brain tumors and normal structures. With an increase in SNR ratio with minimum TR, TrueFISP could also depict the enhancement effect in myoma uteri. True FSIP is a technique that is well suited for cardiac MR imaging. The imaging time is shorter and the contrast between the blood and myocardium is higher than that of FLASH.

See Steady State Free Precession.

Refocused GRE sequences use a refocusing gradient in the phase encoding direction during the end module to maximize (refocus) remaining xy- (transverse) magnetization at the time when the next excitation is due, while the other two gradients are, in any case, balanced.
When the next excitation pulse is sent into the system with an opposed phase, it tilts the magnetization in the α direction. As a result the z-magnetization is again partly tilted into the xy-plane, while the remaining xy-magnetization is tilted partly into the z-direction.
Companies use different acronyms to describe certain techniques.

Different terms for these gradient echo pulse sequences
R-GRE Refocused Gradient Echo,
FAST Fourier Acquired Steady State,
FFE Fast Field echo,
FISP Fast Imaging with Steady State Precession,
F-SHORT SHORT Repetition Technique Based on Free Induction Decay,
GFEC Gradient Field Echo with Contrast,
GRASS Gradient Recalled Acquisition in Steady State,
ROAST Resonant Offset Averaging in the Steady State,
SSFP Steady State Free Precession.
STERF Steady State Technique with Refocused FID
In this context, 'contrast' refers to the pulse sequence, it does not mean enhancement with a contrast agent.