The alkaline batteries that are most equivalent to the LR44 are AG13, L1154, LR1154 and 157. The most common silver oxide battery equivalents to the LR44 are SR44, SR44SW, 303 and 357.
LR44 batteries are alkaline. However, you can use a silver oxide battery equivalent as well. The main differences are that alkaline batteries are cheaper and have a shorter life, and the voltage decreases over the life of the battery. Silver oxide batteries cost more than alkaline and with the price of silver rising, the battery price will continue to go up as well.
If you're using the battery to power toys or lights, an alkaline type works well. However, if you're using it to power an electronic device that requires a steady voltage, the silver oxide battery is a better choice.