The word ころ, often pronounced colloquially as ごろ, means 'around' or 'about' in relation to time. While it functions similarly to くらい, there are some key distinctions. ころ attaches directly to a noun or follows a noun and the particle の.

• ３時(さんじ)頃(ごろ)に会(あ)いましょう。
  Let's meet around 3 o'clock.
• 彼(かれ)は高校生(こうこうせい)の頃(ころ)にアメリカへ行(い)きました。
  He went to America around the time he was a high school student.

A primary distinction between ころ and くらい is that ころ is suitable for indicating a general period in time, whereas くらい is typically reserved for more precise timeframes.

• 学生(がくせい)のくらいはよく勉強(べんきょう)しました。
  When I was approximately a student, I studied a lot. (Unnatural Japanese, as being a student is a general time period)
• 学生(がくせい)のころはよく勉強(べんきょう)しました。
  Around the time I was a student, I studied a lot. (Natural Japanese)

On the other hand, ころ is not used when referring to approximate measurements of distance or length.

• １０ページくらいの所(ところ)を読(よ)んでください。
  Please read around page 10. (Natural Japanese, as an approximation is being discussed)
• １０ページごろの所(ところ)を読(よ)んでください。
  Please read within the span of page 10. (Unnatural Japanese, as this confusingly suggests reading anywhere on the page is fine, rather than near that point)

The underlying reason is that ころ conveys a 'span' of time, whereas くらい refers to an 'extent' or approximation. In this sense, ころ suggests 'during the time of (A),' while くらい is more like 'at the approximate point of (A)'. To illustrate, if we talk about a single day, ころ could refer to the entire morning period (the span), but くらい would indicate a point near a specific time, like 11:50 AM (the extent).

When the time being discussed is already very precise, such as a specific hour, both ころ and くらい can be used naturally. This is because the 'span' and the 'extent' effectively refer to the same narrow point in time.

• 映画(えいが)は８時(はちじ)くらいに始(はじ)まる。
  The movie starts at about 8.
• 映画(えいが)は８時(はちじ)頃(ごろ)に始(はじ)まる。
  The movie starts around 8.