"Lead screw" is a generic term refering to any threaded drive screw using sliding surfaces to transmit a load.
"ACME" is a term that refers to a particular thread form. All ACME screws are also lead screws but not all lead screws are ACME screws. The ACME thread standard is accompanied by specific classes such as 2G, 3G, 2C etc. which have slightly different tolerances. ACME thread forms can be easily checked using readily available thread gauges. The ACME thread standard is designed for interchangeability and manufacturability.
Other kinds of Screws
Static screw applications are generally referred to as fastener screws. They utilize inefficient thread forms to prevent the nut from back driving and are not well suited for regular motion.