In machine learning a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, because such representations are better for numerical processing (dimensionality reduction, find correlations, outliers, similarities etc..) and statistical analysis. In the literature often this vector space that includes all the possible feature vectors from a population of a specific domain, is called feature space.
In machine learning sample space is more or less the same as feature space, but it does not include the interpretation of the vector space. Particularly, a sample space is the space that includes all the possible outcomes in a statistical experiment or another definition could be that is the space of all possible samples that belong to a specific population.