Replying to myself... I think I was not understanding but perhaps now it is clear.
By training fitcsvm with a simple fitcsvm(x,y) I can train the machine with the whole set of data (everything is used as the training set). The trained machine can then be applied to a new (test) data set by the predict function. This is exactly what I need.
Only if I set an option such as 'CrossVal', 'CVPartition', etc, I get a ClassificationPartitionedModel, with a number of machines trained accordingly. Otherwise, I get a ClassificationSVM classifier.
It was simple...
Bye
Giorgio