There are some phone taps that are not true taps at all. They are more like bugs that only allow you to listen to one end of the conversation. While one end can be very useful, the fact is that it can also be very incomplete, leaving a lot of things to conjecture. The most effective phone taps allow you to listen to both ends of the conversation so that you can get as much context from the conversation as possible.
Usually hard taps, soft taps, and advanced cell phone bugs are the phone taps that can allow you to listen to both sides of the conversation. These are taps that get you "into the system," so to speak, so that you are in the middle of the communication. The best and most advanced taps are not noticeable by the parties being listened to, and so the eavesdropper can hear whatever needs to be heard without letting the others know she or he is there.
Hard phone taps are those that make use of an actual physical line. They consist of a secondary line hooked into the primary line and then bridged to another location. The person listening can be at the location of the tap, or they can use a "slave" to send a transmission. This type of phone tap is extremely difficult to detect, as it is hardwired and usually at a location away from the phone, so sweeping the room for bugs will not be effective.
Soft phone taps are those that take place inside the software of the phone company. The listener gains access to the digital network by hacking in or receiving permission. Most phone companies today now incorporate digital lines into their service, even if the person has a land line. This means that the listener only needs to know which line is associated with the conversation he or she would like to listen to. These are relatively easy to find if someone knows how to look in the software, but virtually undetectable to the parties having the conversations.
Cell phone taps are another matter altogether. They make use of a special cell phone that allows you to dial a secret number to activate the phone for listening. The user is usually unsuspecting and has no idea you are listening to the conversation when you use cell phone taps.