ID is between X and Y do include X and Y in results.
ID is after X does not include X.

I know it sounds normal as we said after and after is not including X but i was still surprised by this difference and it is a little bit strange to do searches like ID is after X-1 or ID is before Y+1, it looks a little bit hackish.

I suggest to change behaviour (always include boundaries X and Y) and to therefore rename :

• ID is after X into ID starting from X
• ID is before Y into ID until Y

I do not know what english words would be better though.