No. The English terms "earlier" and "later" refer to the progression of time from the past (earlier) towards the present and future (later); they do not refer to the number itself being larger except incidentally. (The etymologies here are that "earlier" comes from "ere" meaning "before" or "soon", "later" comes from various "lat-" roots meaning "sluggish" or "lazy" hence starting after their appointed time.)
So for example the Wikipedia article on Hellenistic Palestine contains the opening line,
> The region came first under Ptolemaic rule beginning in the late 4th century BCE with Ptolemy I Soter, followed by Seleucid rule beginning in the early 2nd century BCE with Antiochus III the Great.
It then clarifies that the events of the late 4th century BCE include events in ~320 BCE, and that the early 2nd century stuff happened in ~198 BCE. This is a standard usage of those terms "early" and "late" as applied to those centuries, the 4th (400 BCE - 301 BCE) and 2nd (200 BCE - 101 BCE).
I think the issue primarily is that there are two frames of reference used: "earlier" / "later" terms use the absolute frame of reference (time progressing forward), the numerical terms ("100s" / "4th century") are relative to the common era (higher BCE numbers mean further back in time).
To me it is confusing that they've mixed the two, even though it is convention to do so.
So for example the Wikipedia article on Hellenistic Palestine contains the opening line,
> The region came first under Ptolemaic rule beginning in the late 4th century BCE with Ptolemy I Soter, followed by Seleucid rule beginning in the early 2nd century BCE with Antiochus III the Great.
It then clarifies that the events of the late 4th century BCE include events in ~320 BCE, and that the early 2nd century stuff happened in ~198 BCE. This is a standard usage of those terms "early" and "late" as applied to those centuries, the 4th (400 BCE - 301 BCE) and 2nd (200 BCE - 101 BCE).