The speed that you get from your 56K modem is subject to phone line quality. The signal between your home and your phone company's Central Office (CO) is analog. Our connection from the CO to our equipment is all digital and thus lossless.
Remember the radios that used to be in cars? There was a small dial and a vertical bar that you used to tune in a station. A person had to continually tweak the dial to get good reception in the car. Well, remember when car radios went digital and you just punched in the station's numbers and instantly you got optimal reception? That is the difference between analog and digital service. The speed that you see when you logon is your "connect-speed."
The speed of the activities that you do on-line such as page load and downloads are referred to as bandwidth or page-load speeds.
Your real speed varies as the line quality and weather conditions improve or decline. A utility program such as Net.Medic can report the actual data rates being achieved. There is a free "demo" version available for download on-line at www.vitalsigns.com.
The Public Utilities Commission of Ohio (PUCO) guarantees you at least a 14.4Kbps connection. If you routinely see less than that, contact your phone company.