The term “hypnotic suggestions” covers the things the hypnotist asks of the client to experience while being in the hypnotic state of mind. These suggestions can be very direct or indirect, also termed traditional vs. permissive techniques. Straightforward guidance could be something like this: “Your hand will become weightless and rise high in the air,” while the indirect would be something like this: “As you notice a difference in the weight of your hands, one of them may feel so light, that it rices slowly in the air.” Even if I hadn’t labeled these suggestions beforehand, it’s obvious to see which is which.
The direct suggestions represent the classical way of conducting hypnosis, and this will most likely be the style of choice for the stage hypnotist, as it portrays that the hypnotist decides what should happen. Another label for the indirect permissive techniques is Ericksonian hypnosis. Milton H. Erickson is by some considered the father of the permissive methods. His excellent results with using hypnosis to treat various problems have made his name and techniques famous among modern hypnotists.
I think you should avoid hypnotists who state that they are old-school hypnotists or hypnotists who tell you that they are only using direct suggestion. The literature on hypnosis suggests that you are better of with the permissive techniques and hypnotherapy. This is not to say that classical hypnosis doesn’t have any effect, but merely a personal belief that your chances are better with the modern techniques as they involve more of the dynamics of thinking, which we didn’t know about in the past.