Beat frequency is due to interference between two waves of different frequency, and is equal to the difference of the two frequencies.
When two waves of different frequency interfere, there are no stationary waves. Instead, the fringes in the interference pattern are constantly moving in such a way that if you put a tiny detector at a point in the interference pattern, it will observe peaks of intensity passing by at the beat frequency.
You might need to see a stationary wave to understand it. I You can find someone who plays a stringed instrument like a guitar, and ask them to show you how to play harmonics on a string. The point you touch to play any harmonic is a "node" - a place where two waves traveling in opposite directions always cancel out. If there are nodes, we call the wave pattern a "standing wave" or "stationary wave". There can only be nodes when the two waves have the same frequency. The two waves actually only need to overlap to form a stationary wave; they don't need to move in opposite directions.
There are many Youtube videos that illustrate standing/stationary waves, mostly showing waves moving in opposite directions; but all interference patterns consist of stationary waves formed by interference between overlapping waves of the same frequency.