Do synapses have special types? I assume synapses/dendrites/axons are relations which connect one entity/neuron to another, for example:


a car is a vehicle: "is" relation
Bob has a sister: "has" relation
etc.


I would just imagine that when car is fired it would activate the connected neuron vehicle. But how does the brain differentiate between the relation types? What makes it "know" that a car "is" a vehicle and not "has" a vehicle?
This question seems to be asking "How is knowledge represented in neurons" and then jumps to the assumption "synapses represents relations". As discussed in the linked question, there is a lot of evidence that this method of binding is not biologically plausible, given that it doesn't scale well to the level of human vocabulary.

So, to answer your question, it is hypothesised that there are "special" synapses to do certain operations/relations, however the model you seem to be holding in your mind is incorrect. For more information, please check out "How to Build a Brain" by Chris Eliasmith or the other reference below.

Reference

Eric Crawford, Matthew Gingerich, and Chris Eliasmith. Biologically plausible, human-scale knowledge representation. In 35th Annual Conference of the Cognitive Science Society, 412–417. 2013.