All that matters is the English name of the card, not what it does. You can have at most four copies of a card with a given name:
100.2a In constructed play (a way of playing in which each player creates his or her own deck ahead of time), each deck must contain at least sixty cards. A constructed deck can have any number of basic land cards and no more than four of any card with a particular English name other than basic land cards.
The main exception is the basic land cards: Plains, Island, Swamp, Mountain, Forest, the five corresponding Snow lands, and Wastes. The only other time you can have more than four of a given card is when the card itself says so, like Relentless Rats:
A deck can have any number of cards named Relentless Rats.
So yes, you can have four copies each of several different Rat cards: four copies of Typhoid Rats, four copies of Pack Rat, and so on.
And it also doesn't matter if the cards do the exact same thing, as long as the name is different. You can indeed have four Essence Scatter and four Remove Soul..
Of course, you can only have up to four copies of cards you're actually allowed to play. If a card is banned or otherwise illegal in the format you're playing, you can't have any, and if it's restricted you can have only one copy. See How should I determine whether a deck is legal in a particular format? for discussion of that and other deck restrictions.
Finally, there are also some singleton formats like commander where you do construct your deck ahead of time, but the usual four copies rule is replaced by a one copy rule. Again in those cases, only card name matters, so you can have one copy each of several cards that do the same thing.