There's an important footnote with U.S. Customs and Border Protection's data. It states that:
"Apprehensions refers to the physical control or temporary detainment of a person who is not lawfully in the U.S. which may or may not result in an arrest."
Most of the people CBP counts in its data are listed under the heading "apprehensions."
Don't simply say, then, that those who have crossed the southern border and been detained have been "arrested." Not everyone has been, or will be, charged with a crime. The best practice is to use "apprehended" or "detained" as the action words when reporting broadly about what is happening to people. Save "arrested" for those times when we drill down into the data.
About that data:
When reporting on the recent surge of migrants, many of whom are seeking asylum, there are two categories. As mentioned, the biggest category is migrants who are apprehended after crossing the border between official ports of entry without authorization. The second category is migrants who presented themselves at ports of entry without documentation and were deemed "inadmissible."
When referring to the total (the two categories added together), we should say more than 100,000 were "taken into custody" or "detained," and we can refer to the migrants as "unauthorized." There's more guidance on the language around immigration in this earlier post.