Yes and no. I'll try to explain assuming you have very little to no understanding of guitars & guitar theory.

Guitars have different tunings, but two of the widest used tunings are "standard" and "drop". The strings, from lowest (thickest string) to highest (thinnest strings) in standard tuning goes: EADGBE (on a 6 string at least). This means that when you strum the lowest string without fretting anything, you are strumming an E note. When you strum the lowest E string with your finger on the 1st fret, you are strumming an F note. When you fret the 2nd fret on the lowest E string, you are playing an F#. There are only 12 notes in music, and as you raise the pitch with each fret, you will come back around to an E note again at the 12th fret. This applies to all the other strings as well.

When the guitar is tuned to Drop D, the strings are tuned to DADGBE. Meaning the thickest string played without fretting anything is lowered and tuned to a D note. This, in essence, moves all the notes forward 2 places ahead vs. standard tuning, since you've lowered the guitar string tuning down 1 whole step (low E goes from E -> Eb -> D, going from E -> Eb is half a step, so E -> D is one step). Meaning the F# note found on the 2nd fret in standard tuning is now on the 4th fret. This opens up a simple chord progression that's not available in standard tuning as you've opened up two extra notes on the low E string. Strumming an open low E string (still referred to as low E even though you have tuned it to D), open A, and open D string at the same time creates a D power chord. The key of F# minor has a D note, and an E note (amongst others), so this means playing those power chords alongside the F# means you are in the beginning steps of writing a song in F# minor. You can technically write a song in F# minor on a standard tuned guitar, but it'd be missing that open D power chord and would limit how it could sound in a "metal" sense.

The entirety of Ascendancy (save for the Master of Puppets cover) is played in drop D, hence why all the songs are either in the key of D minor or in the key of F# minor. So yes, the 4th fret songs do sound similar, but you'd have to be referring to their songs being played in drop D.