This happened six times throughout the night with my mother and I speaking to each other on the separate phones. One evening we took the cell phone with us to a restaurant. My mother answered the phone and heard her answering message on her home phone. This was confirmed when we got home and checked the messages. My mother's cell phone is through her work and her home phone number is unlisted so there is no record of her home phone number connected to the cell phone, nor has she ever called her home phone with her cell phone or vice-versa.
Electronic equipment operates on different frequencies.
The fine print describes how the appliance is not supposed to interfere with broadcasting or televisions, etc. In the case of your answering machine and the cell phone, both these appliances operate on specific electronic frequencies. If there is an incompatibility, the appliances will either not work or work incorrectly or erratically, especially when within range of each other. That is the reason some appliances do not work when connected with each other. Quick examples include some VCRs which do not work when connected with certain TVs or computers, or some answering machines which do not work when connected to certain telephones or fax machines.