When I first knew my future husband, he had what was known as a tape recorder - although a tape recorder/player might have been a more descriptive name. There was no-one else I knew who had such a thing. He was extremely technically minded, and he built it himself from parts which were available in the sorts of specialist shops which started to disappear as electronic parts became smaller and integrated.
I suppose that ready-made tape recorders must have been on sale, but they would have been very expensive.
The reel-to-reel tape-recorder contraption was a bulky thing, very like the one in the photo. For recording it was used either with a separate large microphone to record what people were saying or singing, or to record music straight from a radio. Playback normally required a separate speaker which was also bulky.
Blank tapes were available for purchase, but I am reasonably certain that there were no music tapes on sale anywhere. These tapes were bulky things, sold open on their reels with no protection other than the reel itself - see the above picture.
In use, a full reel of tape on one side of the machine wound onto an empty reel on the other side. Before re-use, it had to be re-wound.
The tension of the tapes had to be just right. If it wasn't, the tape tied itself up in knots or broke.
Smaller cassette tape recorders/players were about a decade away. At that stage, the older tape recorders/players became known as 'reel-to-reel tape recorders'.