they serve different purposes. Strut and tie bars serve to increase rigidity of the frame, whereas sway bars decrease the sway by acting on the suspension, not the frame.
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ROTOZEY19111 (2:40:30 PM): I bought a bigass can of seafoam TRANNY treatment
ROTOZEY19111 (2:40:51 PM): and put that in my crankcase
Strut bars connect the strut towers. One in the bay and usually one in the trunk or rear deck lid (top). Lower strut bars usually connect 2 points of the chassis underneath the car, most consider them useless.
Swaybars connect the front control arms or rear control arms (usually). They act like springs to reduce body roll and help keep the wheels planted on hard turns, corners.
A tie bar can be thought of as a 'bridge' that connects ('ties' together...hence the name) the mounting points for your suspension. In essence it is a chassis brace that braces the area where the struts and/or suspension arms connect to the chassis. A car will handle best if the chassis is stiff (does not flex) and all of the flexing is done by the suspension itself.