In terms of fat loss, one way of looking at it is this:
One lb per week [/i]of fat loss[/i] is a rate that should pretty easily be attained, without any diet for the diet to go "strange" or be unsustainable. This rate of fat loss can be sustained as long as needed. For example, a person who is about 50 lb too fat would do very well for himself to sustain this for a year. There is no adverse effect on the metabolism at this rate of fat loss.
Roughly speaking, dropping about 500 cal/day below weight-maintaining intake can do this.
Two lb per week of fat loss is harder to do. With enough physical work and close care to the diet it can be done as above but commonly supplementation will be needed, and/or metabolic rate may fall with extended such dieting, and/or the diet may need to be changed to something that wouldn't be sustained for a really long time. If daily calories stay at least, according to a way of looking at it that I prefer, 12 times your in-shape bodyweight, then metabolism should not be harmed. For example, if your in-shape weight would be 200 lb, then 2400 cal/day. If fat loss is falling below goal, increase activity rather than decrease calories below this.
Roughly speaking, this requires being 1000 cal/day below weight maintaining intake, but should NOT be done by reducing calories below the above.
Three lb per week of fat loss is a far faster rate than can be doable as above but is yet more challenging. It represents a practical realistic max for most, though it's not an absolute limit.
Weight loss is a different matter. A person can go on a low-carb diet with carb intake insufficient to meet what the body needs, which results in it burning most of the glycogen (proving the diet is incorrect) and thus lose 10 lb of water weight in a week without, necessarily, much fat loss at all. This is why in the supermarket tabloids you constantly see headlines on how this diet or that diet will lose a woman 10 lb in a week, and also part of why it is difficult to help general female public. The expectation is things such as 10 lb of weight loss in a week, which has nothing to do with an effective fat loss program but everything to do with a water loss program. Sometimes men fall into this trap as well. Weight loss isn't the goal, but fat loss.
(There is also the aspect of muscle loss potentially contributing to weight loss, but with weight training this isn't usually as major an aspect as water loss from overly-low carb intake.)