Brand is intangible, and more emotions based. It’s the feelings, emotions, and experiences a person encounters with your company. Example: Think of someone you know. That persons brand is the “gut” feeling, emotions, and thoughts you have when thinking of that individual.
Identity system is part of the brand. It’s the look/visual/style of the brand. Example: Think of the same person, remove feelings, only think about the way they look, the way they dress, e.t.c. The persons style is his/her identity system.
Logo is a brands mark (visual), and falls under the brands identity system. Example: Your signature is your personal brand mark, you use it for marking important documents. It’s used to verify your authenticity.