We implement solutions. We apply pressure to a wound. We apply principles to a design, strategy or foundation. We apply ourselves to our work.

'Implement' means to put into effect for the first time. 'Apply' means to put something into effect or into use after it was implemented. For instance, on January 1st, a city implements a parking ban on Main Street between the hours of 5 PM and 7 PM. On January 5th, a police officer applies the law and tickets a car which is parked on Main Street between those hours.

Apply means put in practical use. Implement means put into effect. Carry out. The author has tried to paraphrase to make the sentence more understandable.

So there's a INCREDIBLY small but equally important difference between the two. 'Implement' means to put into effect for the first time. 'Apply' means to put something into effect or into use after it was implemented. For instance, on January 1st, a city implements a parking ban on Main Street between the hours of 5 PM and 7 PM. On January 5th, a police officer applies the law and tickets a car which is parked on Main Street between those hours.