Before I reply, I should stress that I'm not a music theorist/historian/expert, and for that matter not much of a keyboardist, so I'm relying heavily on information gleaned from the internet in addition to my own (limited) knowledge and experience. In short, the following information may very well contain misinformation or faulty explanations, but I'll certainly try to avoid that. I also hope that other forum members will jump in and correct any bad information that I might inadvertently spew!
Technically speaking, I don't think an arpeggiator is quite the same thing as a pattern sequencer or step sequencer-- although the term "sequencer" could be used to describe the mechanism by which arpeggios are generated on synthesizers or electronic keyboards, since an arpeggio is a sequence of notes. The way I see it, it's largely a question of how the sequence is triggered and how it's used. That is, an arpeggio is triggered by playing a note or group of notes, and usually stops when you release the notes, whereas a pattern might be initially triggered by playing a note but then usually continues to repeat or loop even after you release that note. Thus, a pattern is a loop (usually one or more measures long) that keeps playing independently of whatever you're playing, although the musical key that the pattern plays in might be controlled by the key(s) you're pressing in the keyboard's "accompaniment" or "left-hand split" zone; whereas an arpeggio is a shorter pattern that starts and stops in conjunction with whatever notes or chords you're playing, so it might repeat for only a fraction of a measure, or for several measures, depending on how long you hold down the keys-- and since the arpeggio is triggered by pressing a key, it can be retriggered several times in a single measure, in time with the notes you're playing.
Historically speaking, "arpeggio" refers to a playing style or technique in which the notes of a chord are played separately (usually in rapid succession) rather than all at once, like a guitarist strumming a chord (i.e., each string gets played at a slightly different time, depending on how fast the guitarist is strumming them), or like a harpist plucking notes at different times (apparently the word "ARPeggio" is derived from "hARP"). Arpeggios-- also called "arpeggiated chords," "broken chords," or "rolled chords"-- are written as a chord with a squiggly vertical line in front of it, which means to play the lowest note first, then the next-lowest note, etc., in rapid succession with a sort of rolling motion of the hand and fingers. In cases where the composer wants the notes to be played in the opposite direction-- i.e., highest note first, then next-highest note, etc.-- there will be a vertical arrow pointing downward in front of the squiggly line. In either case, the notes are held down to form an actual chord-- i.e., you don't play each note and then release it when each subsequent note is played, rather you play each note one-at-a-time but continue holding it down as each of the other notes are added to the chord.
But there can be variations of this-- e.g., the notes of a "chord" might be written as a series of notes (such as eighth notes) in some order that forms a repeating pattern. In this case you play and release each note separately, rather than continuing to hold them down as each new note is added.
"Arpeggios" on the Yamaha PSR-E443 are more similar to the second type, because when you hold down one or more keys (while the Arpeggio feature is turned on) it causes the keyboard to play a short sequence or pattern of notes as though you were playing a series of individual notes. The Arpeggio type determines what kind of pattern is played while you're holding down the note(s). For example, some Arpeggio types may play a repetitive sequence of ascending or descending notes in a certain musical key even if you're holding down just one key, whereas other Arpeggio types may vary the pattern and musical key depending on which combination of multiple keys you're holding down. The PSR-E443's Arpeggio types are categorized according to specific voice types that they're recommended for, such as "piano" arps, "guitar" arps, "clavi" arps, "bass" arps, "synth" arps, "percussion" arps, and so forth-- but you can certainly use a "percussion" arp with an organ voice, or use a "synth" arp with a guitar voice, etc.
I've been out of town and haven't had access to my keyboards, but now that I'm back I'll try to record and post some examples of what the PSR-E443's arpeggios sound like.
Edit: On the PSR-E443, the "step sequencer" is more akin to the auto accompaniment "Styles" and "DJ Patterns," which repeat patterns of notes and percussion rhythms that change musical keys according to the notes you play in the "accompaniment" zone of the keyboard. One important point to make is that the PSR-E443 doesn't let you create your own Arpeggios, Styles, or Patterns on the keyboard, as more expensive arranger keyboards, workstation keyboards, and synths do-- rather, you're limited to the built-in Arpeggios and Patterns, although you can load and use external Styles. Of course, if you're using the PSR-E443 with external software (such as a DAW) then you can potentially create arpeggios and patterns externally and play them back through the keyboard.
Edit #2: Note that there are VST plug-ins and other sequencer software that let you create arpeggios and pattern loops, even if your keyboard doesn't have an arpeggio feature. Thus, if you buy a keyboard that doesn't have an arpeggio feature per se, that doesn't necessarily mean that you can't play arpeggio patterns on it.
