just a unit of measurement.
bit is 1.
byte is 8 bits.
That's correct, but you're using it in the wrong application.
When you're talking about storage, 1 bit is the smallest unit of measurement, but after 8 bits, you never see it referenced. For example, no one would ever describe a hard drive as storing 960Gb (gigabits). You would of course say it is a 120GB (gigabytes) hard drive. Also, because this system is based on powers of two, a kilobyte is 1024 bytes, rather than 1000 as the prefix 'kilo' is normally interpreted as.
When talking about transfer speeds, bits are used, but not in the same way as storage. Because the rate at which data is transfered does not really rely on powers of two, the traditional prefix meanings are used. So, if you see a transfer speed of up to 10Mbs (Megabits per second), it really does mean 10^6 * 10 (10,000,000) bits per second, which would translate into about 1.192MBs (megabytes per second).
While this is somewhat deceiving every ISP in existence does the same thing, so it's not as if you would be fooled if you were comparing speeds of two different providers. However, they are deceiving in the way that they often advertise speeds as being "10 Megs per second" or "10Mb per second" which when heard verbally could mean either 10MBs or 10Mbs.