Basic triad chords are made up from 1, 3 and 5. So in your case, it'll be F# A# and C#. To change the sound from major to minor, the 3 is flattened. So F#m consists of F# A and C#. It's the starting block for most of Western harmony.
The '7' part uses - surprise - the 7th note as well. This is where confusion comes in.There are four simple chords using a 7th of some kind. For simplicity, I'll just use the notes, and not go into theory.
The major 7 uses the major triad plus the major 7th note. F# A# C# E#.
The minor 7 uses the minor triad plus the minor 7th note. F# A C# E.
The dominant 7 uses the major triad plus the b7 note. F# A# C# E.
The minor major 7 uses the minor triad plus maj7 note. F# A C# E#.
When we call a chord simply 'F# seven(th)', the reason is most likely because the dominant seven chord is the most commonly used, so the name gets shortened for convenience.Others will need qualifying.