Q:

QGIS: what is the difference between heatmaps and interpolation plugins? 

I need to generate a raster looking like a « heatmap » based on a points layer.  On this layer, each point represents a nest (bird population study).  I need to produce a nest density map (raster) from this layer.  I noticed that rasters produced from Heatmaps and Interpolation plugins were somewhat similar, so I'm wondering if there is one plugin specifically recommended for what I need to achieve. 
I specifically would like a square-shaped extent (with X,Y mini and X,Y maxi), that Heatmaps plugin does not do (Interpolation does).  I would like this extent to be colored for zero values.  One more thing: I don't have any attribute to be taken into account in my nests layer (Interpolation plugin asks for such an attribute to rely upon). 
Then, I don't really get the difference between the two plugins. 

A:

Heatmaps and interpolations are completely different things though they might look similar.  
A heatmap visualizes "hotspots" in the distribution of features on the map i.e. dense areas will be highlighted in a heatmap, based on the parameters you use for processing it. 
However the purpose of an interpolation is to estimate feature values at locations where no measurement data is available.  If you would for example take a lot of temperature measurements in the field you can obviously not measure the temperature at every single location across the study area (i.e. you can't measure a continuous field).  You would use the interpolation to estimate the temperature values between the measurement points.