Simply put, an APN, or Access point Name, is the name used to identify a GPRS bearer service on the GSM network.
Different APNs can have different configurations like IP ranges (private or public), firewall setup (blocked ports or unrestricted), different proxy configurations, different billing, etc.
For example there are the general purpose APNs like 'internet' and 'MyMTN' which typically allow you to go anywhere, but have restricted incoming connections. Vodacom have an 'unrestricted' APN which gives you a routeable IP address and doesn't block any incoming connections, MTN have 'MTNVPN' which is similar. There are also APNs for other services like MMS and Vlive! which only allow access to the relevant gateways. There are also corporate APNs which do not allow access to the internet, but only to the corporations private network.
MTN's 'internet' and 'MyMTN' APNs are functionally equivalent, in fact, I'm sure one of the reps has even posted here that one is an alias of the other. So you get billed the same and they perform they same, it does not matter which one you use.
It is strange that you are seeing both on your bill though, how sure are you that your SIM is staying inside your modem? Is it possible that someone is using your SIM in another device when you are not around?