In some jurisdictions around the world the buyer / seller relationship is viewed as principal / agent. Under a principal / agent relationship the principal can be sued for the actions of the agent. If those actions are negligent the buyer can be sued under tort law for that negligence. That results in potential liability to the buyer.
If you have language that says that the supplier will be responsible to you for such liability you have a contract commitment that would be enforceable to recover the damages the injured party was awarded. If you have an indemnification, the seller is agreeing to be responsible for that potential liability and you have protection based upon the scope of that indemnification,
If the injured party sued the seller directly and not the buyer there would be no need for an indemnity. What frequently happens is the injured party will either sue the buyer (as the buyer may have more assets (deeper pockets) or they will sue both parties. An indemnification without the obligation of defense simply means that the seller is agreeing to only pay the damages awarded. If the indemnification also included the responsibility to defend, the seller would need to pay for the defense of the claim, or defend against that claim in court with them bearing the costs of the defense or settlement. If you have the obligation to defend and indemnify the seller (indemnitor) has agreed to effectively "stand in your shoes" and manage the process, pay the costs of the defense and pay any damages awarded or settlement amounts.
The value of either language to accept liability or or indemnify is based upon the assets of the party providing that commitment. When you are dealing with small companies it is best to require them to carry certain levels of insurance as additional financial protection such as comprehensive general liability and vehicle liability. Then if there is a claim the insurance company may be involved in the defense and you have the protection of both the insurance amounts and the sellers assets as protection.
The value of either agreeing to accept liability or agreeing to indemnify can be limited by the limitation of liability section as to both the types of damage that may be claimed and the amounts. I would carve either of these commitments out of limitation of liability for that reason. My rationale is simple, if the third party were to sue them directly they would not have a limit on that potential liability.
One last comment from a buyer's perspective you need to be concerned about the language in the section further limiting the value of what they will provide. You see under tort law a third party can sue for negligence. It doesn't require gross negligence or willful misconduct. Ordinary negligence will do. When a seller wants to be liable or indemnify only for "gross negligence or willful misconduct" they are setting a much higher standard that significantly limits the value of their commitment. What that is effectively saying is you need to be responsible for all ordinary negligence claims and I will only be responsible if the claims meet these much higher standards. As a buyer I would want the liability or indemnity to apply to any negligent act, error or omission. Your company didn't cause the injury or damage, they did, so why should you have to be responsible for anything.