The TCP/IP stack is a complete set of networking protocols. The OSI Model was meant to be a standardized way of connecting devices together, and most protocols have some direct correlation to the OSI Model.
The OSI Model as you know has 7 layers, the TCP/IP stack which is the most common Protocol suite in use today has 4.
So the easiest way to look at the TCP/IP stack is to compare them.
Layer Number OSI Model Name TCP/IP Equivalency TCP Protocols at this level
1. Physical Network Access or Interface layer Cables and types of Transmissions (Cat45, FDDI, COAX, RJ11)
2. Data Link Layer Network Access or Interface layer Ethernet
3. Network Internetwork IP (biggest most important)
4. Transport Transport TCP/UDP, Multiplexing, PAR
5. Session Application
6. Presentation Application
7. Application Application
So once you get to layer 5 and above OSI there isn't generally a real sorting of the protocols, but an example of TCP/IP protocols at this layer, some examples include http, ftp, POP3, SMTP, telnet
So what does a model really mean. Well, a model provides a guide to ensure that everything is considered when communications are constructed. That is why the OSI model came to be. Generally when people design applications in TCP/IP they need to get it down to IP and Port Level do the encoding and have it hand over to TCP that will break it into segments and ensure end to end delivery or UDP that will just break it down and send it.
TCP/IP and the OSI model go hand in hand, as do most protocol suites once you understand them, but there is a tonne of study involved in understanding what they actually are. Topics such as IP Subnetting, and Multicast exist because of TCP/IP. NAT/PAT, IPv6. The internet as you know it exists as a direct result of TCP/IP winning as the chief protocol. That's not to say that there isn't other ones out there, just that this is the key one.
I hope this is sorta what you were looking for.
There is no actual manifestation of the OSI Model, just protocols that were designed to handle same layer communications and adjacent layer communications, and deliver your bits around the world.
Finally, TCP/IP was originally designed by the US Military, and Microsoft chose it as its primary protocol, that should tell you why it became so big. But someone had to win. Most of the firsts for TCP/IP was actually implemented in UNIX/LINUX and taken by Microsoft. There are about 100 ways to answer this question, but I think this is what you were looking for mainly.