I'm trying to figure out why some of the text messages on my Android only display the date while others display the time? Do the older messages have the date only?
As FieryCod has already said:
If the message is from today it will show only the time but if it is from earlier it will show the date
As others suggest it is caused by the fact that:
Messages were written/received at present for example you received a message on Monday and till Monday is not end there is no need to show the information about day and month so it is only the hour displayed.
If the Monday is ended and there is a Tuesday now, there is a day displayed, because the message did not come today but one day ago so it is normal to show the day not a hour which might be confusing.