(CE-FFE-T1) A T1 weighted gradient echo sequence.

See Spoiled Gradient Echo Sequence.

Spoiled gradient echo sequences use a spoiler gradient on the slice select axis during the end module to destroy any remaining transverse magnetization after the readout gradient, which is the case for short repetition times.
As a result, only z-magnetization remains during a subsequent excitation. This types of sequences use semi-random changes in the phase of radio frequency pulses to produce a spatially independent phase shift.
Companies use different acronyms to describe certain techniques.

Different terms for these gradient echo pulse sequences:
CE-FFE-T1 Contrast Enhanced Fast Field Echo with T1 Weighting,
GFE Gradient Field Echo,
FLASH Fast Low Angle Shot,
PS Partial Saturation,
RF spoiled FAST RF Spoiled Fourier Acquired Steady State Technique,
RSSARGE Radio Frequency Spoiled Steady State Acquisition Rewound Gradient Echo
S-GRE Spoiled Gradient Echo,
SHORT Short Repetition Techniques,
SPGR Spoiled Gradient Recalled (spoiled GRASS),
STAGE T1W T1 weighted Small Tip Angle Gradient Echo,
T1-FAST T1 weighted Fourier Acquired Steady State Technique,
T1-FFE T1 weighted Fast Field Echo.
In this context, 'contrast enhanced' refers to the pulse sequence, it does not mean enhancement with a contrast agent.

(GRE - sequence) A gradient echo is generated by using a pair of bipolar gradient pulses. In the pulse sequence timing diagram, the basic gradient echo sequence is illustrated. There is no refocusing 180° pulse and the data are sampled during a gradient echo, which is achieved by dephasing the spins with a negatively pulsed gradient before they are rephased by an opposite gradient with opposite polarity to generate the echo.
See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The excitation pulse is termed the alpha pulse α. It tilts the magnetization by a flip angle α, which is typically between 0° and 90°. With a small flip angle there is a reduction in the value of transverse magnetization that will affect subsequent RF pulses. The flip angle can also be slowly increased during data acquisition (variable flip angle: tilt optimized nonsaturation excitation). The data are not acquired in a steady state, where z-magnetization recovery and destruction by ad-pulses are balanced. However, the z-magnetization is used up by tilting a little more of the remaining z-magnetization into the xy-plane for each acquired imaging line.
Gradient echo imaging is typically accomplished by examining the FID, whereas the read gradient is turned on for localization of the signal in the readout direction. T2* is the characteristic decay time constant associated with the FID. The contrast and signal generated by a gradient echo depend on the size of the longitudinal magnetization and the flip angle. When α = 90° the sequence is identical to the so-called partial saturation or saturation recovery pulse sequence. In standard GRE imaging, this basic pulse sequence is repeated as many times as image lines have to be acquired. Additional gradients or radio frequency pulses are introduced with the aim to spoil to refocus the xy-magnetization at the moment when the spin system is subject to the next α pulse.
As a result of the short repetition time, the z-magnetization cannot fully recover and after a few initial α pulses there is an equilibrium established between z-magnetization recovery and z-magnetization reduction due to the α pulses.
Gradient echoes have a lower SAR, are more sensitive to field inhomogeneities and have a reduced crosstalk, so that a small or no slice gap can be used. In or out of phase imaging depending on the selected TE (and field strength of the magnet) is possible. As the flip angle is decreased, T1 weighting can be maintained by reducing the TR. T2* weighting can be minimized by keeping the TE as short as possible, but pure T2 weighting is not possible. By using a reduced flip angle, some of the magnetization value remains longitudinal (less time needed to achieve full recovery) and for a certain T1 and TR, there exist one flip angle that will give the most signal, known as the "Ernst angle".
Contrast values:
PD weighted: Small flip angle (no T1), long TR (no T1) and short TE (no T2*)
T1 weighted: Large flip angle (70°), short TR (less than 50ms) and short TE
T2* weighted: Small flip angle, some longer TR (100 ms) and long TE (20 ms)

Classification of GRE sequences can be made into four categories:

• T1 weighted or incoherent/(RF or gradient) spoiled GRE sequences
• T1/T2* weighted or coherent/refocused GRE sequences
• T2 weighted contrast enhanced GRE sequences
• ultrafast GRE sequences

See also Gradient Recalled Echo Sequence, Spoiled Gradient Echo Sequence, Refocused Gradient Echo Sequence, Ultrafast Gradient Echo Sequence.

(TFE) Turbo field echo is a gradient echo pulse sequence with data acquisition after an initial 180° (similar to IR) preparation pulse for contrast enhancement. The difference between a FFE and TFE other than the speed of the sequence is that the image is acquired while approaching steady state (the echoes are collected during the time in which the tissues are experiencing T1 relaxation).
The contrast is prepared one time, which means the contrast is changing while the echoes are collected and can be manipulated by selecting the type and timing of the prepulse. A delay time is given before the actual image acquisition. To achieve T1 contrast the 180° prepulse is followed by an operator selected delay time, that results in no signal from the targeted tissue. So when the echoes are acquired, no signal is present, additional RF spoiling is performed to optimize for T1 contrast. The delay chosen corresponds to when T1 relaxation reaches and suppresses T1 signal or optimizes the difference between tissues. Contrast for these sequences are enhanced when K-space is filled using a centric or low-high ordering. A TFE can be acquired with a 2D or 3D technique and with or without T1, T2 weighting.
See Ultrafast Gradient Echo Sequence, TurboFLASH and Magnetization Prepared Rapid Gradient Echo (MPRAGE).