Sometimes the number designation refers to the battery's chemistry, i.e.,silver oxide, lithium oxide , mercury, etc. the battery's ,external dimensions will remain constant, but different chemistries were historically associated with specific devices. Watches traditionally use silver oxide batteries, cameras also. But hearing aids or electronic devices might favor mercury or lead batteries. As long as the voltage ( usually 1.5 volts) is the same for the device, they should be interchangeable. Certain older cameras were engineered for 1.3 to 1.35 volt batteries. If you use a modern 1.5 volt battery, the meters are inaccurate. There are websites devoted to making battery shells that have a built in resistor that can reduce a smaller sized 1.5 volt battery down to the 1.35v threshold. In watches, there are also High drain and low drain versions of certain batteries. The high drain types are used in watches with numerous "complications-" stop watch or moon phase dials, etc. if your watch isn't more "complicated" with anything more than a day or date wheel, the low drain versions will suffice. The LR 44 is also known as an Ever Ready 356 or as an A76.
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