As long as you understand that the Federalists were a political party and that federalists are simply people who believe in federalism, you have the basic idea. The only reasons that it is important to keep this in mind are that the Federalists only existed for a short time and that they had beliefs other than a belief in a federal system.
The Federalist Party itself did not exist for very long. At the earliest, you could say that it originated in the early 1780s. The party was dead soon after the War of 1812. So, even though it was an important part of the beginning of our country, it did not last very long.
Second, the Federalist Party held beliefs that really had nothing to do with federalism. Federalism (small f) is simply the idea that there should be some formal division of powers between the national government and the state governments. But the Federalist Party believed many other things. It believed, for example, that America should have a diversified economy that included manufacturing. It believed in supporting England in its war against France. These policies have nothing to do with federalism.
Finally, someone could be a federalist without being a Federalist. We could say someone today is a federalist if they feel that the national government is too strong and that the states need more of their powers back. But this person would clearly not be a Federalist since that party has not existed for almost 200 years.
So, the difference between a Federalist and a federalist are not tremendous, but they do exist and could be important at times.