Answer:
A lobbyist is a professional whose job is to make contacts with influential people in Washington (or whatever government) and make a case on behalf of a client. They're regulated under the Lobbying Disclosure Act of 1995. If you're spending most of your time chatting with Congressmen, then you need to file forms saying who you're talking to and on whose behalf. These forms are filed with the clerks in the House and the Senate.
While a Political Action Committee (PAC) is a group of people with some kind of interest. They collect money and spend it to promote that interest. They have to file forms, with the Federal Election Commission rather than with the legislative branch, though unlike the lobbyists they have ways to not disclose who's giving them money. They can hold public meetings, buy TV advertising, donate money to causes, give money to candidates (a small amount- about $5k to candidates and $15k to parties), and hire lobbyists.
Generally, when a PAC hires a lobbyist, the lobbyist is the one to go to the legislator and make the case on behalf of the PAC. They may also bring the PAC's own team to make the presentation, but they need to be very careful about crossing the (byzantine) set of rules trying to keep the ethical lines clear-ish. Conceivably, they could have lobbyists on staff, but it exposes the entire organization to levels of disclosure that they'd generally rather not have. Thus, the usual plan is for a PAC to hire an established lobbying firm, who is already registered and prepared to handle the paperwork.
Explanation:
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