I was under the imprssion that a strut supports something, whereas a tie holds two object together.
In this case, I think that the 'strut' is actually a 'tie' and is used to transmit aerodynamic loads, ie lift, back to the main fuselage structure.
It probably means that the original horizontal stabiliser structure was a bit too weak and adding a tie was a quick fix to strengthen it.
In the case of a Cessna 150, it may be that the 'strut' supports the wing when its on the ground, but then acts as a 'tie' when the aircraft is in the air. It may be less draggy and lighter to have a strut than to have a bigger wing structure.