Q:

How to classify entire pixels within loaded polygons as a feature collection, in Google Earth Engine

I need to determine the Modis pixels that enter whole within the polygons contained within a feature collection.
I also need to determine those who don't fully enter. 
Apologies for English 
This is the script
https://code.earthengine.google.com/2c58d1f0e127f0d002ed20cf6872fe05

A:

Interesting question. As your feature collection was not shared, I made one myself by drawing four polygons and adding them as import feature.
I believe the solution of Sean Roulet works pretty well, but it will still identify some pixels partly not inside your feature collection as inside, while they are actually not fully inside. 
Therefore I used reduceToVectors. Following the method below, you will make a feature collection getting only the pixels which are fully inside your import feature collection. A disadvantage is that this will easily run out of memory if your area is large.
// make unique vectors from the pixels in the feature collection giving each pixel a random value
var randomImage = ee.Image.random().multiply(100000).toInt().reproject(image.projection())
// give an additional buffer around the area of intrest of the scale to include all pixels
var bufferWidth = 1; // set to 1 (include a buffer of scale size) or higher to lower the buffer
var buffered = poligonos.map(function(polygon){return polygon.buffer(image.projection().nominalScale().divide(bufferWidth))})
var toVectors = randomImage.reduceToVectors(ee.Reducer.countEvery(), buffered);

// calculate the pixels perfectly inside the feature collection of interest
var allVectors = poligonos.map(function(feature){
  // get the geometry of the individual features
  var geom = feature.geometry();
  // map over the pixel polygons
  var pixelPoligonos = toVectors.map(function(pixelPolygon){
    var pixelGeometry = pixelPolygon.geometry();
    return ee.Feature(pixelGeometry, {containedIn: pixelGeometry.containedIn(geom, 1)})
                                    .copyProperties(pixelPolygon)
  })
  return ee.Feature(pixelPoligonos)
}).flatten();

// remove duplicates. First sort on the pixels which are insie to not loose those
var insideAndOutside = allVectors.sort('containedIn', false).distinct(ee.SelectorSet('label')).limit(toVectors.size());
// seperate the polygons inside and outside the area of interest
var outside = insideAndOutside.filter(ee.Filter.eq('containedIn', false));
print('outside', outside)
var inside = insideAndOutside.filter(ee.Filter.eq('containedIn', true));
print('inside', inside)
// add the polygons to the map
Map.addLayer(outside.draw('red'), {}, 'pixels outside as features')
Map.addLayer(inside.draw('green'), {}, 'pixels inside as features')

// clip the images to the feature collections and show on the map
var pixelsInside = image.clipToCollection(inside);
var pixelsOutside = image.clipToCollection(outside);

Map.addLayer(pixelsInside , {palette: ['green']}, 'pixels inside')
Map.addLayer(pixelsOutside , {palette: ['red']}, 'pixels outside')

Note that you will need to determine a 'bufferWidth', which you can set at 1 to determine also pixels only for a little part inside your feature collection. Set it higher (2-3) if you are mainly interested in the pixels actually fully inside your feature collection.
Link to full code.

