I often talk about debt collectors, but many, and perhaps most people being sued for debt are being sued by people (or companies, usually) that have purchased the debt from someone else and are suing to collect the money for themselves. These are sometimes called "junk debt buyers."
There are some companies that collect debts for other companies, taking a percentage of the collections as their fees, and most people think of these companies when they think about "debt collectors." But the term "debt collectors," in its legal sense, is broader than that. There are also debt buyers, who buy the debt from the original creditors and collect on their own behalf, and these companies are also "debt collectors" in the law.
If the company deals primarily with debts generated by another person, it is a “debt collector” whether it is a debt buyer or (just) a collector. So the company that bugs you on behalf of the original creditor is a debt collector, and so is the company that bought the debt and began harassing you in an attempt to collect for itself. And so, usually, are the lawyers suing you and their firms. All must obey the Fair Debt Collection Practices Act.
We distinguish between debt buyers and "actual" debt collectors in the Debt Negotiation Manual for negotiation purposes because they play different roles in negotiation, but under the Fair Debt Collection Practices Act they are all the same.