> Lobbyists make more money, because they lobby on behalf of clients for the money, while think tanks do it for the ideology.
Think tanks often do it for the money, too; the difference is that lobbyists directly and overtly represent clients to policy makers in seeking change, while think tanks tend both to minimize their direct link to funders and direct their output to the public (in theory), though it often ends up as material that allied lobbyists present to policy makers.
If the interests backing them were sovereign states, then (in terms of their role in promoting policy) lobbyists would be ambassadors, and think tanks would be "public diplomacy" operations.