A warm lead is a prospect who has already shown some interest in your product: visiting your pricing page, downloading a resource, or replying to a campaign. The warmth comes from their own behavior, not from a person who introduces you.
The two get conflated, but the warmth comes from different places. A warm lead is a status the buyer earned through their behavior; a warm introduction is a mechanism, where a trusted connector hands you the access. One signals interest; the other transfers trust. For the full contrast, see warm lead vs. warm intro.
A warm lead may know your product but still has no reason to trust you, so the conversation can stall. A warm intro starts from trust, which is why it tends to convert higher. The strongest motion is a lead who also arrives through a warm path.
Via adds the missing layer to your warm leads: a route in. When a lead shows interest, Via shows you whether someone in your network can introduce you, so you can follow up with trust behind the message instead of a cold reply.