A routing protocol lets network routers automatically share information about which paths are actually available and agree among themselves on the best route for data to travel toward its destination, without requiring a human to manually configure every possible path by hand. Different routing protocols, OSPF and BGP among them, exist because routing data around inside a single organisation's own network and routing data between entirely separate, mutually distrustful networks scattered across the internet turn out to be genuinely different problems, each needing its own specifically suited protocol.
Routing inside one organisation can trust every router to cooperate fully
OSPF is designed to operate inside a single organisation's own network, where every router genuinely belongs to the same administrative authority and can be trusted to share accurate, complete information about the network's actual layout. Under that assumption of full mutual trust, OSPF routers can share detailed information about the entire network topology and calculate genuinely optimal shortest paths using that complete picture, an approach that works well specifically because there's no need to guard against a router lying or an unauthorised network unexpectedly joining the conversation.
Routing between separate networks has to assume nothing of the sort
BGP instead handles routing between separate, independently operated networks across the wider internet, where no single organisation controls or fully trusts every other network involved, and where each network legitimately wants to advertise only limited, policy-controlled information about its own routing preferences rather than its complete internal structure. BGP is built specifically around exchanging that more limited, policy-filtered routing information between mutually independent networks, a genuinely different design problem from OSPF's single-trusted-organisation assumption, which is exactly why the internet relies on these two structurally different kinds of routing protocol operating together rather than one single protocol handling both jobs.
What we're still unsure about
That OSPF and BGP are built around genuinely different trust assumptions, full internal trust versus mutual independence between separate networks, and that this difference justifies using structurally different protocols, is well established, confirmed networking practice underlying the actual functioning internet. What's more genuinely an ongoing security and engineering concern is exactly how to make BGP's inherently trust-limited routing announcements more reliably verifiable, since BGP was originally designed without strong built-in mechanisms for confirming that a network's routing announcements are actually legitimate, and network engineers continue to develop and deploy additional security measures to guard against genuinely disruptive routing misconfigurations or malicious announcements, rather than that vulnerability being fully closed off already.
This sits inside Routing Protocols (OSPF, BGP), one of seven topics in Networking, one of seven domains in Computer Science, one of seventeen subjects the app can quiz you on.