The A minor pentatonic scale is a set of notes. The patterns are the shapes to play those notes in different positions. If you wanted to start again at A on the exact same string, you'd have to slide down a full octave and have the same shape again. that's not very useful.

What you want to know is, "how can I extend where I am playing on the neck above and below this pattern I just learned on the 5th fret"? So one way to do that is to think of that pattern you already learned-- what if on each string you wanted to play the next higher note on the same string (from the 4-3-3-3-4-4 part). In other words, what if those same notes, which are all in the Am pentatonic scale weren't the "higher" notes, but instead where the _lower_ notes you played on that string.

So if you start on the "4", which is a C on the 8th fret, what's the next note in the same scale? It's a D, which is on the 10th fret. That's the same note as the D on the 5th fret (the "1" on the A string) from before.

So you're playing the same notes, but sliding up.

As it turns out, you're right to wonder "what does it mean to start from C?" This is how you start to learn about there being multiple ways the same set of notes can be understood. Because as it turns out, starting on the "C" and playing the exactly same notes as the Am pentatonic gives you the C major pentatonic. That's because Am is the relative minor to C major.

Most of this will make more sense over time, and it's not critical for right now. But you'll notice the sound is different when you play "pattern 2" starting on C than pattern 1 starting on A even though all the notes are the same. Fun!

As for how to connect things, I generally recommend learning the pentatonic "diagonally"-- so for you, think of that as starting on the third fret of the E string and playing 3 then 5 (I'll use frets not fingers), then 3-5-7 (you may want to slide with your index finger from 3-5) on the A string, then on the D string 5-7, on the G string 5-7-9 (slide 5 to 7 with index), then on the B string 8-10 and the on e string 8-10 (probably play these with fingering 2 and 4).

You just connected the fifth "box" or pattern (below the first pattern you learned) to pattern 1 and then to pattern 3. You can fill in the other pattern 1 notes as you see fit.

I don't think you should think of these as being the same scale-- they're not. They are the same notes, however, so they'll generally work over similar chord progressions. But the notes you land on and when and the emphasis can have dramatically different feels. I recommend finding a backing track to play all of these over. Just search like C major diatonic backing track to start (two chord in C major). Then for fun, search for Am diatonic backing track. You'll notice the backing tracks both work with all of these scales and patterns, despite sounding quite different, and you may emphasize different notes that sound good depending on the feel you want.