To answer your question directly, there is indeed a huge difference between fast cuts and slow cuts. The first point I'm making will point you to a very clear study about it.
To add more on it, here is a bit more detailed answer.
There are multiple factors to consider when planning a diet:
I Rate of weight loss
Studies have shown that there seem to be an optimal threshold with which fat loss was optimal in regards to lean body mass. It is said that 0.7% of body weight loss a week is optimal.
II Protein intake
According to this study, a combination of high protein diet and resistance training is the best way to conserve muscle when trying to lose weight.
A diet high in protein is key during prolonged weight loss
Sleep is a huge factor. This article is about a study where they compared the rate of fat loss between people sleeping 5.30 hours a night versus 7.30 while being on the same caloric intake. They found a tremendous difference between the two, in favor of the more sleep group.
Multiple styles of training exist. This paper argues that Aerobic training is the best regarding weight loss while resistance training is optimal for conserving muscle mass.
I hope this helped !