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.

(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.

(SFP or SSFP) Steady state free precession is any field or gradient echo sequence in which a non-zero steady state develops for both components of magnetization (transverse and longitudinal) and also a condition where the TR is shorter than the T1 and T2 times of the tissue. If the RF pulses are close enough together, the MR signal will never completely decay, implying that the spins in the transverse plane never completely dephase. 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, then the flip angle for steady state should be 45-60°.
Steady state free precession is also a method of MR excitation in which strings of RF pulses are applied rapidly and repeatedly with interpulse intervals short compared to both T1 and T2. Alternating the phases of the RF pulses by 180° can be useful. The signal reforms as an echo immediately before each RF pulse; immediately after the RF pulse there is additional signal from the FID produced by the pulse.
The strength of the FID will depend on the time between pulses (TR), the tissue and the flip angle of the pulse; the strength of the echo will additionally depend on the T2 of the tissue. With the use of appropriate dephasing gradients, the signal can be observed as a frequency-encoded gradient echo either shortly before the RF pulse or after it; the signal immediately before the RF pulse will be more highly T2 weighted. The signal immediately after the RF pulse (in a rapid series of RF pulses) will depend on T2 as well as T1, unless measures are taken to destroy signal refocusing and prevent the development of steady state free precession.
To avoid setting up a state of SSFP when using rapidly repeated excitation RF pulses, it may be necessary to spoil the phase coherence between excitations, e.g. with varying phase shifts or timing of the exciting RF pulses or varying spoiler gradient pulses between the excitations.
Steady state free precession imaging methods are quite sensitive to the resonant frequency of the material. Fluctuating equilibrium MR (see also FIESTA and DRIVE)and linear combination SSFP actually use this sensitivity for fat suppression. Fat saturated SSFP (FS-SSFP) use a more complex fat suppression scheme than FEMR or LCSSFP, but has a 40% lower scan time.
A new family of steady state free precession sequences use a balanced gradient, a gradient waveform, which will act on any stationary spin on resonance between 2 consecutive RF pulses and return it to the same phase it had before the gradients were applied.
This sequences include, e.g. Balanced Fast Field Echo - bFFE, Balanced Turbo Field Echo - bTFE, Fast Imaging with Steady Precession - TrueFISP and Balanced SARGE - BASG.

See also FIESTA.