What’s the difference? They seem the same to me.
Biological weapons are alive, usually bacteria (Anthrax, Smallpox…etc), hence “biological.”
Chemical weapons are things like teargas, mustard gas…etc. Man made.
The line can be sort of blurry. Botulinum toxins are often classed as “biological” weapons, as they are produced by a living organism, but they aren’t actually living organisms themselves, but more like a bacterially-derived “nerve gas”.
In practical terms, there are a couple of potential differences between biological and chemical weapons. One is that chemical weapons (including botulinum toxins) have immediate effects, whereas infectious biological agents (germs) will generally have an incubation period and those persons who are exposed to them won’t show the effects for days, weeks, or even months. This makes biological weapons probably less useful in military terms, but perhaps more useful to terrorists.
The other main difference is the potential of biological weapons to make more of themselves. “Nerve gas” doesn’t manufacture more of itself after it’s dropped on the enemy, but bacteria or viruses potentially can reproduce and spread from a small initial infection to a massive plague. Theoretically, biological weapons could be as catastrophic as nuclear weapons, maybe more so, and self-replicating biological agents would be even more susceptible to “blowback”–killing off your own side–or affecting neutral countries than nuclear weapons. Not all infectious biological weapons have this property; anthrax does have an incubation period, but the spores won’t reproduce themselves–although they may remain in the targetted area and be able to cause infection if the target isn’t decontaminated–and anthrax doesn’t generally spread by person-to-person contact. Something like smallpox, on the other hand, or even more so some hypothetical genetically enhanced version of smallpox or another infectious agent, would be a really monstrous thing to unleash on the human race.
You can find out more about biological and chemical weapons at the Federation of American Scientists’ “Introduction to Special Weapons” page.