I think your "three types" are TRCC, TBCC and RBCC. But be aware that these three are the ideas from the late 1990s. Since then lots of new ideas have come around.There are only three types of combined cycle engines. Are there any more?
There has been many improved variants of them that one may regard as different types such as SABRE which adds a precooler to mitigate the thrust gap of classic TBCC. Whether that precooler is a change big enough to make SABRE related by separate type than TBCC is up to personal opinion. There is also TRRE which has ducted rocket inside the scram/ram channel, it is essentially a cross-breed of TBCC and RBCC, so it deserves its own type. Then we have detomation combustion engine which therotically can start from zero speed to hypersonic, this may greatly reduce the usage of turbine or remove it all together.