The difference between the first and second link is that the first two are standard electromagnetic relays (the clicking sound you’ll often hear when appliances turn on is this type of relay switching). It will take 2-12v DC input for the signal (so will work with the spark, photon, arduino, etc.) and can switch up to 15 amps (which should be plenty for a fridge, especially if it has a starter capacitor. I would buy the normally closed version so if it fails the fridge stays off and the beer comes to room temperature (rather than cold crashing), up to you though.
The second link uses a solid state relay (SSR), which has silent operation but can sometimes have overheating problems. These are what Elco sells in the store here. The silent operation is especially nice for brewpi’s heater control because the relatively shorter PWM cycles would have the heater relays clicking on and off every few seconds. The cooling control has a much longer PWM cycle so it’s less of a problem–plus the fridge probably has an electromagnet relay build it so it will click anyway when it turns on. That said, this particular SSR cable only gives the max continuous load capacity and mentions “non-inductive” which means resistant load applications like lighting or heating vs. inductive loads such as motors (ie. fridge compressors). I don’t know if this means that it has a different rated load capacity for inductive loads, or if it is not intended to be used for inductive loads at all. Easiest thing to do would probably be to contact the customer service of that site, explain your use case, and then let them recommend a model for you.