AG13 is also called: AG13, LR44, LR154, A76, EPX76, 157, 303, 357, 1128MP, 208–904, A-76, A613, AG14, AG-14, CA18, CA19, CR44, D76A, G13A, G13-A, GDA76, GP76A, GPA7, GPA75, GPA76, GPS76A, KA, KA76, AG76, L1154, L1154C, L1154F, L1154G, L1154H, LR44G, LR44GD, LR44H, MS76H, RW82, SB-F9, V13G, 357A, NSN: 6135-99-792-8475 (alkaline)

Is this equivalent to SG13, SR44, SR44SW, PR44, PX76A, PX675A, RPX675?

It will fit. It will work. However, they have different chemistries, which may impact how long the battery lasts. For example, a silver oxide battery (name starting with S) will last longer and give more constant power than an alkaline battery (starting with L). Although it may work, be aware that it may reduce the play time.

It is often used in: Toys, Digital Thermometer, Calculator, Lasers, Flashlights, Security System Panel, Wrist Watches, Medical Devices and Instruments, Memory Backup Systems