I can only partially answer this question, as an Egyptologist, with little experience in near Eastern cultures. However, I'll try to give you as best as answer I can from my experience.
In Egypt, 'magic' was linked very closely to medicine and religion. Magicians could have multiple roles, and often used ivory 'wands' (which imo looked more like boomerangs). These wands were, as I said, curved ivory pieces, and were often carved with images of protective demons or gods, for example Bes, a household minor god.
One main issue with looking at 'magic' in Egyptology is the differentiation between magicians and priests, and whether there is even one to be made. For example, lector priests often performed spells and rituals, invoking hka (Heka), a magical power which is also the name of a deity associated with magic. However, whether magic was restricted just to priests is unclear, as you also have spells in the Book of the Dead and the Coffin and Pyramid Texts. This implies that anyone can invoke magic with the right spells. There's quite a blurry area here in terms of what defines a 'magician'.
In terms of your question - no, magicians did not perform 'tricks' like we would imagine them today. In Egypt, magicians/priests would perform spells and rituals, mostly associated with death. For example, the Opening of the Mouth ritual, which allowed the ba (soul) of the deceased to exit the tomb during the day through the burial shaft, receive offerings of food and libations, and return to the body at night. Furthermore, spells are useful for the deceased after their death - the Book of the Dead is an entire book of important spells dedicated to making sure a dead individual makes it to the afterlife intact. You have the Heart Scarab spell, 30b in BD, which would be inscribed onto a large Scarab amulet and placed over the heart. It essentially told the heart not to betray its owner - to not be heavy when weighed against the feather of truth.
So in conclusion, no, magicians in Egypt at least were definitely not like ones we imagine today. Magic was part of religion and culture - it was a way to help the sick, to ensure the deceased had a good afterlife, to perform rituals in funerary and temple contexts. Wands were used but not often, but have been found in tombs so possibly are more ceremonial than practical. The abundance of spells we have from funerary texts implies that magic could be performed by anyone, not just lector priests.
For further reading, I recommend looking at the works of Jan Assmann, who is one of the greatest Egyptologists of his time and has published extensively on Egyptian funerary rituals and art. I've also linked a few useful articles too. I've also recommended Shaw's Oxford History, as it's an excellent reference book for everything Egypt related, an encyclopedia of sorts for Egyptologists. Hope you found this interesting!
Assmann, J., 2005, Death and Salvation in Ancient Egypt, Cornell University Press.
Shaw, I. (ed.), 2000, The Oxford History of Ancient Egypt, Oxford University Press.
Example of a heart Scarab from John Hopkins University: http://archaeologicalmuseum.jhu.edu/the-collection/object-stories/ancient-egyptian-amulets/heart-scarab/