MCP is giving the agents a bunch of functions/tools it can use to interact with some other piece of infrastructure or technology through abstraction. More like a toolbox full of screwdrivers and hammers for different purposes, or a high-level API interface that a program can use.
Skills are more similar to a stack of manuals/books in a library that teach an agent how to do something, without polluting the main context. For example a guide how to use `git` on the CLI: The agent can read the manual when it needs to use `git`, but it doesn’t need to have the knowledge how to use `git` in it’s brain when it’s not relevant.