What are the differences between triacs?
A triac is just a three terminal semiconductor device. Electrically, you only really need to consider two states - off and on.

In the off state it must withstand a certain voltage across its terminals without conducting. That's the 600V rating.

In the on state it must withstand a certain current through it. That's the 4A rating.

To go from the off state to the on state it must be triggered by a gate current. That's the "gate trigger current" you see in all the datasheets.

So your target device, the BT134-600E, has ratings 600V/25A/4A/10mA for off voltage, on current peak, on current RMS and trigger current respectively. The first option in your list, the MAC97A6, has corresponding ratings 400/8/0.6/5. It has lower off state withstand and lower on state withstand. It requires less trigger current, but should be dismissed due to its lower withstand ratings.

Continue that assessment for all your other options looking for something with sufficient withstand ratings, and a low enough trigger current. Once you have a shortlist you can start to look closer at other ratings that might be relevant, such as thermal impedance, mechanical fit, etc.