What are hazardous and non hazardous batteries?

Anything that can hold an electric charge can be hazardous if the positive and negative terminals aren't protected against shorting. Secondly, if damaged in any way (usually a dent for the typical cylinder or rectangle batteries) the anode and cathode may come in direct contact and possibly create an explosive pressure release, fire, etc. This is true for nicd, nimh, Lion, Lithium Primary, lead acid, wet cell, dry cell, and any other configurations I can think of (I'm sure there's some exception somewhere). Improper storage such as in a damp area, or hot area can escalate corrosion and shorts can develop with fire, explosive pressure release, and dangerous gas emissions as possible results depending upon battery type.

With that said, batteries are approved for transportation by passing a varying set of tests usually including pressure tests, drop tests, shorting tests, and many more either completed by, or for the manufacturer. A consumer can legally trust what the manufacturer claims, as long as the manufacturer actually makes the correct claims, like storage instructions, installation instructions, handling warnings, transportation restrictions. A no name great deal on egobayazon may not make any claims about their safety at all, so beware! these no name replacement batteries (cell phone, laptop, etc) have been the cause of numerous emergencies globally.

So, to answer your question directly, all batteries can be hazardous, and should be considered so unless the manufacturers instructions have been followed and the battery is in good (has power) condition...and pick a trustworthy manufacturer.