Essentially, lowercase 'b' means 'bit'. A 'bit' is either a 1 or a 0. A 'byte' consists of 8 of these 'bits'. For example: 01000000 is a byte, consisting of 8 bits.

You've got it: one bit is an eigth of a byte. Be careful when comparing speeds and sizes, as a difference of magnitude-eight is pretty significant.

b = bit
B = Byte
Kib = kibibit
kb = kilobit
KiB = kibibyte
kB = kilobyte
Mb = megabit
MiB = mebibyte
MB = megabyte
Gb = gigabit
GiB = gibibyte
GB = gigabyte
Tb = terabit
TiB = tebibyte
TB = terabyte

... as far as speeds are concerned:

bs = bit/s
Bs = Byte/s
Kibs = kibibit/s
kbs = kilobit/s
KiBs = kibibyte/s
kBs = kilobyte/s
Mbs = megabit/s
MiBs = mebibyte/s
MBs = megabyte/s
Gbs = gigabit/s
GiBs = gibibyte/s
GBs = gigabyte/s
Tbs = terabit/s
TiBs = tebibyte/s
TBs = terabyte/s

Usually your ISP will advertise your speed in in Mb/s(megabits/s).

For example your package with 20Mb/s is actually about 2.6MB/s. (Megabits -> Megabytes)

1000 bit = 1 kilobit
1000 kilobit = 1 megabit
1000 megabit = 1 gigabit
1000 gigabit = 1 terabit

1024 bits = 1 kibibit
1024 byte = 1 kibibyte
1024 kibibyte = 1 mebibyte
1024 mebibyte = 1 gibibyte
1024 gibibyte = 1 tebibyte

8 bit = 1 byte
1024 byte = 1 kilobyte
1024 kilobyte = 1 megabyte
1024 megabyte = 1 gigabyte
1024 gigabyte = 1 terabyte

1 kilobit = 1024 bit = 125 byte
1 megabit = 1024 kilobit = 125 kilobyte
1 gigabit = 1024 megabit = 125000 kilobyte
1 terabit = 1024 gigabit = 125000000 kilobyte

Hopefully by now you have the gist of thigns. Here are a few examples for some known connection packages:

256kilobit/s(256kbs) = 32kilobyte/s or 32kB/s or
512kilobit/s(512kbs) = 64kilobyte or 64kB/s or
768kilobit/s(768kbs) = 96kilobyte or 96kB/s or
1mbit/s(1mbs/1mbits) = 125kilobyte or 125kB/s or
10mbit/s(10mbs/10mbits) = 1250kilobyte or 1250kB/s