You really should take a book or use wikipedia, but I will give you an answer.

SEM means scanning electron microscope and means a vacuum machine with an electron beam that scans over a sample. The primary information is given by an everhard thornley detector which gives for each primary beam position an amount of secondary electrons coming from the sample. From that you get an image.

BSE means backscatter electron image. In comparison with the secondary electron image described before the information comes from greater depth. Usually you see in the SE image a topography contrast and in the BSE image an element contrast. The primary beam is scattered at the atom cores of the sample and the heavier the atom the more electrons are backscattered.

EDS means energy dispersive x-ray spectroscopy. You look at the characteristic x-rays which are created by the primary beam in the sample. For each beam position you get a full x-ray spectrum. You can quantify the spectra down to ~0.1% and get element mappings. The lateral resolution is about 1µm.

EPMA means electron probe micro analysis. It is also called WDX (wavelength dispersive x-ray spectroscopy). You need very high current of the primary electron beam and you can only detect a single x-ray energy. But you get the advantage of much better detection limits compared to EDS and much better energy resolution in the spectrum.

EBSD means electron backscatter diffraction. The sample must be flat and tilted to 70°. The EBSD-detector is a phosphor screen which collects the diffraction pattern of the sample, the so called kikuchi pattern. You can get information about the crystal structure and the orientation of the grains in your sample. The technique is very surface sensitive and therefore the samples need usually a special preparation. But the lateral resolution is in the order of magnitude 10 to 30 nm.

In practice EDX is on nearly all SEMs, BSE on most, EPMA and EBSD is special.

You really should take a book or use wikipedia, but I will give you an answer.

SEM means scanning electron microscope and means a vacuum machine with an electron beam that scans over a sample. The primary information is given by an everhard thornley detector which gives for each primary beam position an amount of secondary electrons coming from the sample. From that you get an image.

BSE means backscatter electron image. In comparison with the secondary electron image described before the information comes from greater depth. Usually you see in the SE image a topography contrast and in the BSE image an element contrast. The primary beam is scattered at the atom cores of the sample and the heavier the atom the more electrons are backscattered.

EDS means energy dispersive x-ray spectroscopy. You look at the characteristic x-rays which are created by the primary beam in the sample. For each beam position you get a full x-ray spectrum. You can quantify the spectra down to ~0.1% and get element mappings. The lateral resolution is about 1µm.

EPMA means electron probe micro analysis. It is also called WDX (wavelength dispersive x-ray spectroscopy). You need very high current of the primary electron beam and you can only detect a single x-ray energy. But you get the advantage of much better detection limits compared to EDS and much better energy resolution in the spectrum.

EBSD means electron backscatter diffraction. The sample must be flat and tilted to 70°. The EBSD-detector is a phosphor screen which collects the diffraction pattern of the sample, the so called kikuchi pattern. You can get information about the crystal structure and the orientation of the grains in your sample. The technique is very surface sensitive and therefore the samples need usually a special preparation. But the lateral resolution is in the order of magnitude 10 to 30 nm.

In practice EDX is on nearly all SEMs, BSE on most, EPMA and EBSD is special.

Thank you very much Martin Arndt for the description.