What's the meaning of "not just"?

Question

Could you please tell me what the meaning of "not just" here is?

I certainly didn’t sound like them, and not just because they were British. Their speech had a lilting cadence that made me think of singing more than speaking. Educated by Tara Westover

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I find in two online dictionaries the meanings below for "not just":

• used to say that one thing is true and that another thing is also true.

EX: She's not just my friend, she's my lawyer. 1

• not only

EX: It’s not just me. Other people are complaining too. 2

but I don't know for certain if they fit with the phrase or not. Does it simply mean?

I certainly didn’t sound like them, because:

(1)they were British

[moreover] (2)their speech had a lilting cadence that made me think of singing

more than speaking.

Could you help me please to find an exact answer?

Answer 1

I dressed in dark colors for my first lecture, hoping I wouldn’t stand out, but even so I didn’t think I looked like the other students. I certainly didn’t sound like them, and not just because they were British. Their speech had a lilting cadence that made me think of singing more than speaking. To my ears they sounded refined, educated; I had a tendency to mumble, and when nervous, to stutter.

Means:

I didn't sound like them but I can't say that the only reason why I didn't sound like them is that they were British. In addition to this reason, Their speech had a lilting cadence that made me think of singing more than speaking. To my ears they sounded refined, educated; I had a tendency to mumble, and when nervous, to stutter.

An example,

I didn't like him but not just because he was rude. He was also uneducated.

Means:

I didn't like him because he was both rude and uneducated.