Lerp - Linear interpolate
This takes two values (a,b) and blends between them with an alpha.
The easiest way to think about it: imagine A in a layer in Photoshop, and B is the layer above it. Alpha is the opacity and transparency of that layer.
Put in a white value into alpha and you will get 100% B, black 100% A, and gray - some blend of the two.
The linear part just means there is no ease-in or ease-out of the blend. A value of 0.1 gray in the alpha is 10% B and 90% A.
Power is not the same as erode. Power comes from the math function of the same name (sometimes written as x^y)
Power takes the input and multiplies it by itself an exponent number of times.
If your input is between 0 and 1 this is an easy approximation of contrast, and will make a linear blend have some amount of ease in.
Noise texture - this will be a texture that has some amount of random or chaotic values across it. In VFX usually tiling. This is a cheap way to create the appearance of randomness in a texture. A classic example is the Generate Clouds function in Photoshop.
Distortion - usually relates to distorting a texture with another texture. in unreal for example, if you same one noise texture that is panning across a surface, you can. Take that result and add it to TextureCoordinates to distort another texture.
So usually Panner > Noise Texture > multiply by distortion amount > add TexCoords > Texture Sample 2
Sometimes distortion has other meanings, but in this context usually we are talk about distorting a texture.
(Note it doesn’t need to be a noise texture you use, anything you do that modifies the input uvs of a texture sample is probably distortion, noise is just the most common)
There is a handy thread on this site for dictionary like questions.