Fet is field effect transistor, the generic name for a gain device
based on the electrostatic modulation of conductivity in the channel
between source and drain.
JFET is a junction fet. The isolation between gate and channel is a
reverse biased PN junction. These are depletion only devices
(normally on, turned off by gate bias voltage). They make good low
noise small signal amplifiers, though there is nothing in principle
that prevents them from being scaled up to power devices. They are
functionally similar to triode vacuum tubes at low drain voltage and
more like pentodes at higher drain voltage, if you happen to be
familiar with this older technology.
MOSFET is metal gate isolated from the channel by semiconductor
oxide. They can be made as normally on (depletion mode) devices like
JFETs but are most often made as enhancement types (normally off but
turned on by gate voltage. They can even be made about half way on and
gate bias can turn them on more or turn them off. These are made in a
wide range od device sizes, for small signal through high power
devices, but, by far, the greatest numbers are used for high density
logic devices like microprocessors and gates. I think that MOSFETS
are often noisier than otherwise similar JFETS.