When Is It Better To Use A for in pairs loop, vs a regular for loop?

What Wicked said was incorrect, you can loop through a table with a normal for-loop like this:

table = {"one", "two", "three"}

for i = 1, #table, 1 do
print(table[i])
end

Which would print out:

one
two
three

To answer your question:

The difference between a numeric for loop and a pairs for loop is that a pairs for loop only accepts arrays.

When using a numeric for loop to iterate through a table, it would only give you the index, and you'll have to manually fetch the value from the table using the index, but when using a pairs for loop it would directly give you both the index and the value for that index, like so:

local myTable = {"hello", "my", "dude"}

--Numeric for loop
for i = 1, #myTable do
    print("Index "..i.." is assigned the value "..myTable[i])
end

--Pairs for loop
for i, v in pairs(myTable) do
    print("Index "..i.." is assigned the value "..v)

There's also another thing: a numeric for loop takes less time to run than a pairs for loop.

A simple script would prove this:

myTable = {"one", "two", "three"}

local duration1 = tick()

--Pairs for loop
for i, v in pairs(myTable) do
    print(i)
end

duration1 = tick() - duration1
print("The pairs for loop took "..duration1.." seconds to loop")

local duration2 = tick()

--Numeric for loop
for i = 1, #myTable, 1 do
    print(myTable[i])
end

duration2 = tick() - duration2
print("The numeric for loop took "..duration2.." seconds to loop")

Which would output the following:

one
two
three
The pairs for loop took 0.0014321804046631 seconds to loop
one
two
three
The numeric for loop took 0.0012853145599365 seconds to loop

(The normal for-loop and the in-pairs loop were both tested in two separate scripts, but I merged them together here)

See the difference?

Another example here, the exact same test was conducted, but both of the loops iterated through a folder containing three Parts inside of Workspace

These were the results:

Part (x3)
The pairs for loop took 0.0021255016326904 seconds to loop
Part (x3)
The numeric for loop took 0.0017952919006348 seconds to loop

Conclusion

A numeric for loop should be used when iterating through a range of numbers and a pairs loop would be more convenient when iterating through a table, as it gives you both the index and the value. A numeric for loop is also helpful when time is important.

(I encourage you to research more about this.)