A short code is a five digit number (such as 20880), which can be used to both send and receive messages from users in lieue of long-form numbers. It is usually an easy to remember number allowing two way communication between companies and their clients.
Premium Rated Short codes allow you to generate revenue either from SMSes sent to your number (MO-Mobile Originating), or by charging users for sending SMSes to their phone numbers (MT-Mobile Terminating). The revenue is calculated on the basis of the cost to the user against a revenue share formula.
An alphanumeric is a custom sender id that is registered with Mobile Service Providers and that can be stamped on SMS messages being sent out to users. Once you purchase an alphanumeric, you will have the option of using it as the sender id for messages originating from your account.
Keywords are used to access shared Short Codes. Usually, there are two types of short codes dedicated and shared short codes. Dedicated solely belongs to you while shared is used by multiple users via a keyword. It is a fairly cheap alternative for users who are not ready to deploy Dedicated Short Codes.