I see you mentioned a ‘GTO’. earlier...
Thyristors (by their original definition), are a DC control component...
Triacs are bidirectional thyristors intended for AC...
They aren’t the same as you discovered with your quarter cycle switch!
A lot of people use the names interchangeably- which the actual parts aren’t!
SSRs can be made from either - depending on the application, and may have the zero-crossing detection within the component packaging.