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.

In simple ultrafast GRE imaging, TR and TE are so short, that tissues have a poor imaging signal and - more importantly - poor contrast except when contrast media enhanced (contrast enhanced angiography). Therefore, the magnetization is 'prepared' during the preparation module, most frequently by an initial 180° inversion pulse.
In the pulse sequence timing diagram, the basic ultrafast gradient echo sequence is illustrated. The 180° inversion pulse is executed one time (to the left of the vertical line), the right side represents the data collection period and is often repeated depending on the acquisition parameters.
See also Pulse Sequence Timing Diagram, there you will find a description of the components.
Ultrafast GRE sequences have a short TR,TE, a low flip angle and TR is so short that image acquisition lasts less than 1 second and typically less than 500 ms. Common TR: 3-5 msec, TE: 2 msec, and the flip angle is about 5°. Such sequences are often labeled with the prefix 'Turbo' like TurboFLASH, TurboFFE and TurboGRASS.
This allows one to center the subsequent ultrafast GRE data acquisition around the inversion time TI, where one of the tissues of interest has very little signal as its z-magnetization is passing through zero.
Unlike a standard inversion recovery (IR) sequence, all lines or a substantial segment of k-space image lines are acquired after a single inversion pulse, which can then together be considered as readout module. The readout module may use a variable flip angle approach, or the data acquisition may be divided into multiple segments (shots). The latter is useful particularly in cardiac imaging where acquiring all lines in a single segment may take too long relative to the cardiac cycle to provide adequate temporal resolution.
If multiple lines are acquired after a single pulse, the pulse sequence is a type of gradient echo echo planar imaging (EPI) pulse sequence.

See also Magnetization Prepared Rapid Gradient Echo (MPRAGE) and Turbo Field Echo (TFE).

(CPMG) This type of spin echo pulse sequence consisting of a 90° radio frequency pulse followed by an echo train induced by successive 180° pulses and is useful for measuring T2 weighted images. It is a modification of the Carr-Purcell RF pulse sequence, with 90° phase shift in the rotating frame of reference between the 90° pulse and the subsequent 180° pulses in order to reduce accumulating effects of imperfections in the 180° pulses. Suppression of effects of pulse error accumulation can alternatively be achieved by switching phases of the 180° pulses by 180°.

Pulse sequences, designed to be insensitive to flow, e.g. at every even echo, a spin echo sequence is not flow sensitive. Velocity compensation is achieved by using gradients, which are either symmetrical around a 180° pulse and switched on twice as is the case for motion compensated spin echo pulse sequences, or two antisymmetrical gradient lobes without 180° pulse, which is the way to produce a velocity compensated gradient echo pulse sequence.
The signal of the second echo (and all other even echoes) is independent of the velocity of the object. Thus, velocity-based motion effects stemming from the entire voxel or from spins within a voxel (intravoxel incoherent motion) are suppressed with such pulse sequences.
If higher order motion is relevant, as it may be in turbulent jets across valves, acceleration and jerk effects can also be compensated for by the use of appropriate combinations of gradient- and radio frequency pulses.
With the increasingly stronger gradients, echo times in MR systems can be shortened to the point at which effects other than velocity effects hardly ever become relevant.

(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.