Alpha terminals are located on every Alpha and do offer slight bonuses to production, recycling, refining, prototyping, repairing and reverse engineering. Alpha 1 terminals only offer a few boni, some even offer none while all Alpha 2 Islands offer a set bonus of 50 points to every of those. The Bonus to production improves with a higher relation to the owning faction of the outpost. You increase this relation by doing missions. In addition you will receive the very basic assignments from Alpha terminals, to receive NIC, tokens and a relationbonus.
Beta terminals are outposts which are captureable by doing special SAPs. Once a corporation captured an outpost and brought it over 50%, they can set dockingrights, To corp only, allied, neutral or above and everyone. By that you can lock hostile corporations out of your terminal and decline them to pick up their stuff or start attacks on you from your own terminal. A terminal needs to hit 0% before it can change the ownership. In addition every Sap, no matter if it was done by a player or the SAP timer run off, will drop a specific loot, and the corporation owning the terminal will earn money from actions that non corporationplayers do (for example productionfees)