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.

(CRISP) A specific pulse sequence, wherein the application of strategic gradient pulses can compensate for the objectionable spin phase effects of flow motion.

(Dual/FFE) A FFE technique with simultaneously acquired in and out of phase gradient echoes.

See Dual Echo Fast Gradient Echo.

(DE FGRE, Dual/FFE, DE FFE) Simultaneously acquired in and out of phase TE gradient echo images. To quantitatively measure the signal intensity differences between out of phase and in phase images the parameters should be the same except for the TE.
The chemical shift artifact appearing on the out-of-phase image allows for the detection of lipids in the liver or adrenal gland, such as diffuse fatty infiltration, focal fatty infiltration, focal fatty sparing, benign adrenocortical masses and intracellular lipids within a hepatocellar neoplasm, where spin echo and fat suppression techniques are not as sensitive. Specific pathologies that have been reported include liver lipoma, angiomyolipoma, myelolipoma, metastatic liposarcoma, teratocarcinoma, melanoma, haemorrhagic neoplasm and metastatic choriocarcinoma.

(FGRE) The fast gradient recalled echo sequence belong to the refocused gradient echo sequences.

See Gradient Echo Sequence.

(FFE) An echo signal generated from a FID by means of a bipolar switched magnetic gradient. The preparation module of the pulse sequence consists of an excitation pulse. The magnetization tilts by a flip angle between 0° and 90°.

See Gradient Echo Sequence and Refocused Gradient Echo Sequence.

(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.

(FLARE) Fast Low Angle Recalled Echoes is a gradient echo sequence, typically with low flip angles and refocused gradient echo.

See also Refocused Gradient Echo Sequence and Flip Angle.

(FAST) A gradient echo sequence with steady state free precession.

See Gradient Echo Sequence and Steady State Free Precession.

(GFEC) A contrast enhanced gradient echo sequence.

See Contrast Enhanced Gradient Echo Sequence and Refocused Gradient Echo Sequence.

(IR FGR) A gradient echo sequence with an inversion pulse.

See Gradient Recalled Echo Sequence, Inversion Recovery and Steady State Free Precession.

(ROAST) A gradient echo sequence.
See Refocused Gradient Echo Sequence and Steady State Free Precession.

(F-SHORT) A gradient echo sequence.

See Coherent Gradient Echo and Refocused Gradient Echo Sequence.

(SFP or SSFP) Steady state free precession is any field or gradient echo sequence where the TR is shorter than the T1 and T2 times of the tissue.
The flip angle and the TR maintain the steady state. The flip angle should be 60-90° if the TR is 100 ms, if the TR is less than 100 ms, than the choice of the flip angle for steady state is 45-60°. The T1 weighting is controlled by TR and flip, the T2 weighting increases with the TE. Common TR is between 20 - 50 msec.

(STERF) A gradient echo sequence.
See Refocused Gradient Echo Sequence.