Real time rendering is where the 3D scene renders whilst it is being built in real time (hence why its called real time rendering), which is mostly used for things like video games but is now slowly making its way into other industries such as film, T.V. and architectural visualisation etc. where as offline rendering is where the scene is rendered after it the scene has been built, this is the traditional way or rendering and it is the most common form of rendering for film, T.V. and architectural visualisation at the moment.
Real time rendering is performance focused, meaning that the quality of the image may not be as high quality as offline rendering. This is due to the fact that the higher quality the scene, the more processing power will need to be used up to render out the scene, which will cause less power being put towards the performance. so image quality is sacrificed to optimise performance. With offline rendering however, the performance isn't an issue as the scene is rendered after the scene is built either as an image or a video, instead of the whole scene having to be rendered as its running. This means because there is little to no performance needed with this type of rendering, the render output can be as high quality as possible. One of the biggest advantages that real time rendering has over offline rendering is that the because of the fact that is constantly rendering as its being worked on, the lighting, models and textures ect. are being displayed exactly as they will be in the game/video which can lead to mistakes and issues being spotted and dealt with much quicker and to a better standard. Offline rendering however, doesn't have this benefit as the scene isn't being displayed in a rendered state as it can only be seen in a rendered state when the render button has been hit. Because of this, only what is in frame will be rendered and that's all that can be seen, so if there is any problems, it could take a bit longer to sort out as every time a change is made, the render button has to be hit to render the image out and then view to see what the change looks like.
The time to render is a lot longer with offline rendering. With real time rendering, when the final scene/video/still is being rendered, the scene doesn't need to render it but only export the video frame etc. Offline rendering on the other hand, has to render out each frame from scratch as it goes meaning that rendering videos can take hours (depending on the quality of the machine being used, quality of the render and how long the video is). This means that when working on a project, the render time will have to be taken into account which can result in less time to actually work on the scene/model.