Synapses are formed outside the neuron in the extracellular space (ECS), at the end of axon terminals called "boutons" which are essentially storehouses for vesciles which are tiny packages containing neurotransmitters. The internal mechanisms of the neurons as well as ongoing biochemistry at the location of a synapses "guides" the transfer of proteins necessary for strenghening of removal of these synapses.

So its possible that both mechanisms occur simultaneously, there's just not enough evidence to clearly understand these (yet).