(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).

(BTFE) A gradient echo pulse sequence with a balanced gradient waveform and data acquisition after an initial preparation pulse for contrast enhancement.

See Steady State Free Precession (SSFP) and Balanced Sequence.

This family of sequences uses a balanced gradient waveform. This waveform 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. A balanced sequence starts out with a RF pulse of 90° or less and the spins in the steady state. Prior to the next TR in the slice encoding, the phase encoding and the frequency encoding direction, gradients are balanced so their net value is zero. Now the spins are prepared to accept the next RF pulse, and their corresponding signal can become part of the new transverse magnetization. If the balanced gradients maintain the longitudinal and transverse magnetization, the result is that both T1 and T2 contrast are represented in the image.
This pulse sequence produces images with increased signal from fluid (like T2 weighted sequences), along with retaining T1 weighted tissue contrast. Balanced sequences are particularly useful in cardiac MRI. Because this form of sequence is extremely dependent on field homogeneity, it is essential to run a shimming prior the acquisition.
Usually the gray and white matter contrast is poor, making this type of sequence unsuited for brain MRI. Modifications like ramping up and down the flip angles can increase signal to noise ratio and contrast of brain tissues (suggested under the name COSMIC - Coherent Oscillatory State acquisition for the Manipulation of Image Contrast).
These sequences include e.g. Balanced Fast Field Echo (bFFE), Balanced Turbo Field Echo (bTFE), Fast Imaging with Steady Precession (TrueFISP, sometimes short TRUFI), Completely Balanced Steady State (CBASS) and Balanced SARGE (BASG).

(FSPGR) A sequence similar to TurboFLASH or Turbo Field Echo.

See also Spoiled Gradient Echo Sequence and Ultrafast Gradient Echo Sequence.

(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.