The reason why people sometimes used these two terms interchangeably is that they are similar in terms of meaning, but there are still some differences between the two. When you talk of a beat, you are actually referring to the pace, tempo of a piece.
Most times, the term metronome is used to represent the beat, most especially when you consider some of these western songs. With a metronome, you can be having a constant number of pulses per minute. It has to be constant, whether it is 60 minutes per minute, or not. With this, you would be flowing with whatever you are playing at a constant pace.
At times, you see people referring to the beat of a piece using certain time signatures. While rhythm may have the same explanation as beat, it is usually determined by checking the accent and length used for notes that are played in a piece. This means the rhythm of a piece has something to do with the pitch and the length of the notes. This means the rhythm can vary, but the beat of a piece is usually constant.