Difference between Hz and bps
There are actually three terms you want to know about

Bandwidth

Bandwidth is measured in Hz. It describes the frequency band that a communication channel is able to transmit with low loss. 

Typically we talk about a 3-dB bandwidth, meaning the range of frequencies a channel can transmit with less than 3 dB of loss. For a baseband system, the bandwidth extends from 0 Hz to a frequency B which we call the bandwidth. For a modulated system if the carrier is at f0, then the transmission band would be from \$f_0 - B/2\$ to \$f_0 + B/2\$.

Also, outside of information theory, the term bandwidth may be used more broadly as a synonym for bit rate, or for data processing capacity, but when the units are Hz, we know we're talking about the analog bandwidth of a signal path of some kind.

Baud

You didn't ask about this, but its also important to keep this separated in your mind from the other two terms. Baud is the number of symbols transferred per second on the channel. 

Bit rate

Bit rate indicates the amount of information transferred on a channel, and is measured in bits per second or bps. Bit rate is different from baud if more than one bit is transferred per symbol. For example, in a 4-level amplitude modulation scheme, each symbol can encode 2 bits of information. Alternately, for example when an error-correcting code is used, the bit rate can be less than the baud rate, as a larger number of symbols are used to convey a smaller number of bits of independent information.

The Shannon Theorem shows how bit rate is limited by bandwidth and the signal-to-noise ratio of the channel:

\$C = B\ \log_2(1 + \mathrm{SNR})\$

where C is the capacity (maximum bit rate of the channel), B is the bandwidth of the channel, and SNR is the signal to noise ratio.