Botox, Azzalure and Dysport are trade names for Botulinum Toxin, and these are the products that I use in my practice. From a pharmacological point of view they are similar. There are some other Botulinum Toxin products that I do not use: Xeomin and Myobloc.
I use Azzalure for most facial cosmetic treatments, unless the client requests that I should use another product. I use Dysport for hyperhidrosis treatments, mainly because the amount of product used is more than for the facial cosmetic treatments, and Dysport comes in a vial containing a larger dose.