Baluns are 3-port devices featuring 180 degree phase split.   Hybrid transformers are 4-ports devices featuring two 180 degree ports and an isolated port.  

The origin for the names hybrid transformer and hybrid coil to describe a 3-winding transformer, are apparently lost in early telephone history.  Quite annoying, since the name hybrid carried over to microwave networks as hybrid junction, hybrid network, or just hybrid.  Even more annoying, something called a microwave hybrid can be  referring to 3-port as well as a 4-port device, and might not feature 180 degree split but 90 degrees (a quadrature split), instead, or even 0 degrees (an in-phase split).

The two presentations below provide an overview of ideal baluns and 180 degree hybrids in circuit simulations.

In 1968, Bell Labs engineer Eugene Sartori published a paper compiling a variety of Hybrid Transformer circuit configurations and applications.  It contains 10 figures.  The presentation below shows simulation results for each of the figures.