First, AISI no longer maintains standards for steel chemical composition, so there is no such thing as AISI 1144. The grade 1144 appears in a number of standards, such as the following:
SAE J403 - Chemical composition only
SAE J935 - High strength die-drawn bar standard, with 1144 being one of the grades
ASTM A 29 - Hot rolled bar standard, with 1144 being one of the grades
ASTM A 108 - Cold drawn bar standard, with 1144 being one of the grades
The choice of ASTM standard depends on the product form (cold-drawn bar, hot-rolled wire rod, etc.) that is required.