There is no text justification property in ArcMap. Instead, there is horizontal and vertical alignment. Both parameters are text symbol properties.
By baseline type, there are three kinds of annotation in ArcMap: one-point, two-point, and splined. Splined annotation will not be discussed in this article.
Changing horizontal alignment does different things to one-point and two-point annotation. When you convert labels to annotation, all annotation created has a two-point baseline. With two-point annotation, text is placed along a line; the concept of alignment only has meaning when you have more than one line of text (i.e., stacked text). See the related document below titled "Changes to some label text symbol properties aren't reflected on the map" for further information.
If you have one-point annotation, changing the horizontal alignment changes the position of the text with respect to the insertion point. This behaves very similarly to coverage annotation in ArcInfo Workstation.
Put another way, there is a concept of an insertion point for one-point annotation but not for two-point annotation.
One-point annotation is created in ArcMap in the following two scenarios:
1) When you convert from coverage annotation. See the related document below titled "How are $JUSTIFY and $ALIGN translated when converting coverage annotation to Geodatabase annotation?" for further information.
2) When you use the Text creation tools on the ArcMap Draw toolbar. New text created using the Draw toolbar tools, with the exception of the Splined Text tool, is always one-point text.