For me, the big difference is the intended outcome.
When wearing a bikini, you can expect to get wet.
While wearing lingerie, you expect to get laid.
Girls feel exposed in see-through lingerie because their entire body is on display. In a bikini their most intimate parts are covered. And in many if not most cases, a bikini is worn in public where other women are wearing something similar. None of these women are expecting men to approach them and undress them at a swimming pool or on the beach.
Lingerie is typically worn behind closed doors. Women wear lingerie because in many cases they are hoping that men will undress them.
These are vastly different expectations.