The file extension you see, like .mp4 or .mkv, is called the container — it describes how audio, video, and subtitle streams are packaged together, not how they are compressed.
The codec is the actual compression method used inside that container, such as H.264 or H.265. Two files with the same extension can use very different codecs, which affects both file size and the hardware needed to play them smoothly.
Newer codecs typically offer better compression, meaning smaller files at similar quality, but they can require more processing power to decode. If a downloaded file plays choppily, it is often the codec — not the container — that is the limiting factor on older hardware.