Let's see what each of them stands for -
MBps = Mega Bytes per second
Mbps = Mega bits per second
So, the difference is between bits and bytes. Yes.
1 Byte = 8 bits
1MBps = 8Mbps
That is eight times the difference. This is true for all units mentioning bits and bytes like kbps, gbps, tbps etc.
1KBps = 8kbps
1GBps = 8Gbps
1TBps = 8Tbps
Why is my internet speed 8 times less than what I pay for?
This is certainly a very confusing terminology and I have seen a lot of people complain about it. Some may think they have super high speed internet because they got the plan which offers the highest speed - 100Mbps, but since 100Mbps is only 12.5MBPS in theory and about 10MBPS if you factor in some bottlenecks, then the user may feel that he is being cheated with 10 times less speed than what he paid for. For comparison, the copying speed of a good Hard disk is about 100MBps(Mega Byte).
Note that Internet service providers, mobile companies, networking companies and any telecom company will always tell the speeds in Mbps. Download managers, torrent software, file managers and such stuff generally show the speed in MBps. This is why you often see your download speed to be more than eight times lesser than what your ISP promised.
Note that sometimes the people working at ISPs also get confused by this terminology and they may advertise their speeds as MBPS, MBps, Mega Bytes per second etc, but it is very likely that the person who made that ad was mistaken and what they meant was Mega bits per second.
If you often forget this terminology, then just remember that marketers always use the number which is BIG and attractive.