An analog tape machine, such as a cassette, simply changes the signal into a corresponding magnetic signal which is recorded on a tape. This simply means that, at regular intervals, the voltage is measured and assigned a number. Bit depth refers to the quantity of ones and zeros used in each sample. The higher the bit depth, the more accurate the sound is. A standard audio CD has a bit depth of 16.
Sample rate refers to how often the voltage of the analog signal is measured.
One of the rules of digital audio is that the highest frequency you can record digitally is exactly half of the sample rate. So, if you are using a sample rate of 48 kHz, then the highest frequency you can record is 24 kHz. Well, there is a strong debate going on as to whether or not it makes any audible difference. The argument goes that the filters at 20 kHz to 24 kHz cause distortion in the audible range, and that you are removing some overtones of instruments that will affect the overall sound of the instruments. If your sampling frequency is 88.2 kHz, then you can let all audio up to 44.1 kHz pass.