Although different, they are often used interchangeably.

I used to work in a coffee house which I have squeeze limes. Whenever there is an order for lemon or lime juice, it is also the same juice mix. Never heard any customer ever complained.

Fresh lemon juice smells different from limes, calamansi, our local lime and kaffir lime. Each hold a different fragance, and ripe calamansi actually it less sour and a subtle sweetness.