They both mean medium, so they are probably the same. Are they?
Usually they are the same thing. FYI，if 载体carrier is something, Media媒介 is everything. whole meaning on media: http://www.businessdictionary.com/definition/media.html
carrier, mostly means practical channel like radio, newspaper, internet,etc.
So in this point the meaning are the same, means of communication, as radio and television, newspapers, and magazines, that reach or influence people widely
just like English, Chinese language's words and expressions are used in circumstances and may link to different aspects as the context changes.
载体 is more related to carrier, bearing something on it, holder of something, while 媒介 is more related to medium, pipe, conducting something, or the intermediate interface between things.
载体: [used more in circumstances related to material or things or physical constructs. more as a carrier] 媒介: [used more in circumstances related to human, social, media, and interpersonal relationships. more as an interface]
Very interesting! Both semantics and syntax mixed up in here.
載體 is a noun. It is the thing which moves a to b; definitely a new sounding word, yet I found one example from 1965!
In biology, such as virology or genetic technology, 載體 is a "vector", so we have words like 病毒載體 viral vector, for which there is a Chinese wikipedia article. It is also used in transportation, and the example from 1965 refers to a rocket "carrier" for a satellite where a stage failed to separate. It is a term of art, and this already makes it very different from 媒介.
But there are important differences in meaning as well. Here is an example where 媒介 works and 載體 doesn't:
沒有第三國為媒介，日本政府仍舊能夠以其他方法將上述態度通知俄國... Even without a third country as an intermediary, Japan can still still express its views to Russia by other means.
Nothing is being carried, so 載體 doesn't work. Here 媒介 means to act as intermediary, not as a carrier. Here is another example:
人與神交往，就以血作為媒介 When men and gods interact, they do so through the medium of blood.
This is talking about the use of sacrificial blood to communicate with gods. There is no "intermediary" here, but 'blood' is clearly an intermediate mechanism or means for the communication. "medium" fits here, but 載體 doesn't.
Unlike 載體, 媒介 can also be a verb. Here is an example that took some time to find:
蜜峰因採蜜而媒介了花粉，動機還不是由於自私. Honey bees convey pollen through collecting honey (?) and their motive is by no means selfish.
載體 is impossible here. Perhaps we could translate this as "convey"? It can also be used for more abstract ideas:
資訊網最新的網路交易市場功能，更為國內廠商媒介了三萬多個商機 The information network's latest online exchange market functions has also introduced over 30,000 business opportunities for domestic manufacturers.
Here "媒介" is really close to its original "matchmaker" sense. Anyway, an interesting contrast. Good question.