It is a classification of the mode of production. However, you are quite right in saying that property relations for the proletariat are not fundamentally different under capitalism than, say, feudal society.
One can as such absolutely draw a parallel between a serf and a wage labourer in this regard, but equivocating the two, like you do, is utter nonsense.
Similarly, using this parallel to conclude that we are not living under a predominantly capital mode of production is rubbish, justifying the recommendation of reading.