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I have been wondering this for a while. What is exactly the difference between a translucency shader and a transparency shader?

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Transparency allows light to pass through without refracting or scattering it, while translucency scatters light to some degree.

What the wiki says about the Transparent shader:

Transparent BSDF without refraction, passing straight through the surface, as if there was no geometry there. Useful with alpha maps for example. This shader affects light paths somewhat differently than other BSDF's. Note that only pure white transparent shaders are completely transparent.

The Translucent shader is more like a Refraction shader with a high Roughness and an IOR of 0 (no refraction) It is also a little bit like an SSS shader in that light is scattered when passing through. (The main difference between the two is that the translucent shader scatters light more uniformly)

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To visualize this using the wiki images:

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