Assume that category_id is an index key (not primary key) of table books. Is there any difference between the following two SQL statements?
SELECT * FROM books WHERE author='Bill' AND category_id=1
SELECT * FROM books WHERE category_id=1 AND author='Bill'
I guess filtering records first by category_id and then by author is faster than filtering them in reverse order. Are SQL engines smart enough to do it this way?
In short, no, they do not matter as the optimizer will determine the best means for fetching the data.
No, the order of the WHERE clauses does not matter.
The optimizer reviews the query & determines the best means of getting the data based on indexes and such. Even if there were a covering index on the category_id and author columns - either would satisfy the criteria to use it (assuming there isn't something better).
SQL is declarative.
In your example, you have told the engine/optimizer what you want... it will now work out the best way to do that (within reason and "cost" which would be off topic).
Whereas in general, no, that assumes you're using a modern database. Maybe ten years ago, it certainly mattered then.