When I read the role descriptions here, http://dota2.gamepedia.com/Role, it seems unclear to me as to what the difference is between a Lane Support and Support.
Support
"Can focus less on amassing gold and items, and more on using their abilities to gain an advantage for the team."
Supports are heroes whose purpose is to keep their allies alive and give them opportunities to earn more gold and experience. Supports will usually come with skills, such as healing spells or skills that disable enemies; and generally have low damage output (but often with a powerful-yet-situational ultimate). Like Semi-Carries, Supports are not dependent on items (with some exceptions), and thus, most of their gold will be spent on items for the benefit of the team such as Animal Courier, Observer Ward, Sentry Ward, and Smoke of Deceit. Supports are typically paired with the team's Carry at the start of a game. This is because the Carry tends to be the weakest and most gold-hungry member of the team early on, whereas support heroes are at their strongest in the early game. A Support should always forfeit kills to any teammates who are more reliant on items than s/he is, only performing a kill if none of his/her allies are able to do it.
Lane Support
"Helpful in the early-game laning in protecting your team's carry."
Lane Supports or Babysitters are Heroes who help their team's Carry control the lane in the early stages of the game. They are able to either repel enemies from your team's carry and thus keep them safe, or to allow the carry to continuously stay in the lane using abilities that replenish either health or mana. Common traits of Lane Supports are long-ranged right-click attacks and abilities that are highly useful from level 1 and up. They should always lane with the team's Hard Carry, as aside from supporting them, their lack of dependence on gold and levels means said Carry can take all the farm for themselves without running the risk of soloing a lane.