The gas trimix is a mixture of 3 gases, oxygen, nitrogen and helium and heliox is a mixture of helium and oxygen.
The main difference between the two is the presence of nitrogen in trimix and the absence of the same in heliox.
The use of nitrogen in trimix reduces the amount of helium that has to be mixed in the mixture. This reduces cost as helium is a very expensive gas. The use of nitrogen is also helpful in alleviating High Pressure Nervous Syndrome that can occur when scuba diving to depths greater than 130 m.
The absence of nitrogen in Heliox prevents the loading of tissues as unlike nitrogen, helium can be desaturated from tissue at a very fast rate.
The effects of the addition of Helium are the same in both the gases.