Selecting the best software for both screen recording and live streaming depends on your specific needs and preferences. As of my last knowledge update in September 2021, "OnTheFly" was not a widely recognized term in this context. However, I can provide recommendations based on popular and well-established software options that excel in these areas.

OBS Studio (Open Broadcaster Software):

OBS Studio is a powerful, free, open-source software that is highly regarded for both screen recording and live streaming. It offers a range of features, including:

Flexible Screen Recording: OBS Studio allows you to capture your entire screen or specific application windows. You can adjust recording settings for optimal quality.
Live Streaming Capabilities: It supports live streaming to platforms like Twitch, YouTube, and Facebook Live, offering various customization options.
Scene Management: You can create and switch between scenes, making it easy to transition between different screen captures or camera angles during a live stream.
Audio Mixer: OBS Studio features an audio mixer to control audio sources, making it ideal for balancing game sounds, microphone input, and other audio elements during live streams.
Plugin Support: You can extend OBS Studio's functionality with a variety of plugins to enhance your recording and streaming experience.
Streamlabs OBS:

Streamlabs OBS is a user-friendly, free software based on OBS Studio, tailored specifically for content creators. It offers:

Streamlined Interface: Streamlabs OBS simplifies the setup process with a user-friendly interface, making it accessible to beginners.
Alerts and Overlays: It provides a wide range of customizable overlays and alert widgets to enhance your live streams.
Integrated Chat and Dashboard: Streamlabs OBS includes integrated chat and a dashboard for managing your streaming activities.
Built-in Themes: You can choose from pre-designed themes to quickly give your stream a professional look.
Multistreaming: Similar to OBS Studio, Streamlabs OBS supports multistreaming to reach multiple platforms simultaneously.
When choosing between OBS Studio and Streamlabs OBS, consider your level of experience and your specific streaming and recording needs. Both are excellent options and offer robust features.

For "OnTheFly," if it's a new software or service that has emerged since my last update, I recommend researching it separately to assess its features, user feedback, and how it compares to established solutions like OBS Studio and Streamlabs OBS for your screen recording and live streaming requirements.