"Sophistry is deliberate and fallacy is non-deliberate".
A fallacy can be employed intentionally or unintentionally. 'Sophistry' typically implies intent.
A fallacy occurs when an argument relies upon an error in reasoning.
From Logically Fallacious:
The word "fallacy" comes from the Latin "fallacia" which means "deception, deceit, trick, artifice," however, a more specific meaning in logic (a logical fallacy) that dates back to the 1550s means "false syllogism, invalid argumentation."
A logical fallacy as a concept within argumentation that commonly leads to an error in reasoning due to the deceptive nature of its presentation. Logical fallacies can comprise fallacious arguments that contain one or more non-factual errors in their form or deceptive arguments that often lead to fallacious reasoning in their evaluation.
An example of a fallacy is a non-sequitur:
When the conclusion does not follow from the premises. In more informal reasoning, it can be when what is presented as evidence or reason is irrelevant or adds very little support to the conclusion.
Example: "This car's engine is the same engine they use in a Ferrari. Therefore this car is as fast and as high quality as a Ferrari".
A salesperson might deliberately construct such a fallacy (perhaps to deceive), or they might unintentionally use it because they are convinced that it is true.
The use of clever but false arguments, especially with the intention of deceiving. Also, a fallacious argument. (Oxford languages).
Sophistry typically implies intent and is therefore a deliberate act. The salesperson in the above example might reasonably be described as a sophist if she was intentionally using a limited amount of data (the Ferrari engine) to persuade a potential buyer that a lesser car powered by a Ferrari engine was actually as fast and as high quality as a Ferrari. As Conifold points out in the comments section, the term 'sophist' would be even more apt if she habitually used this argument and other fallacious arguments to persuade customers into purchases.
Note however that according to Study.com, there are 3 types of sophistry:
Sophistry by Accident. Example: "Cutting a person with a sharp instrument is a crime. Doctors do this. Therefore, doctors commit crimes".
Sophistry of the Irrelevant Conclusion. Example: "Peter cannot win that football match. He is unfriendly and grumpy" (a non-sequitur).
Sophistry of Many Questions in One. Example: "How can you continue to evade so many taxes?" (when it has not yet been established that taxes are being evaded. The question essentially assumes an answer to one question, "Are you evading your taxes?", and adds another, "How can you continue to evade them?".
Sophistry is disturbingly prevalent in contemporary culture, including in the behaviour of a variety of contemporary news and current affairs outlets, and in the commentary of politicians; institutions and people upon whom we would like to be able to rely upon for truth.
One of the best ways to learn to protect yourself from the dangers of sophistry is to familiarise yourself with a range of common logical fallacies. Here are 22 Common Fallacies.