No, 3/4 guitars do not need different strings than full-sized guitars. You can see sets of strings marketed as 3/4 size strings but this is largely a marketing tactic.
What matters the most is the string material, tension and thickness. It is also important to be aware that certain string characteristics vary between different brands, so it might take some trial and error to find a set that feels right for you.
When you are looking at strings for your 3/4 size guitar these are the things you need to consider:
Guitar String Material (Steel/Nylon)
Nylon string guitars and steel string guitars are built differently, and you should not use strings steel strings on a nylon string guitar and vice versa.
Nylon strings are rated in terms of their tension. The three classifications are light, medium and high tension. This tension has an impact on the volume produced by the string (the higher the tension the louder the string), and also the tone. The higher tension strings are supposed to have a brighter sound.
However, be aware that this increased tension does mean they will require extra effort and strength to push down on the fretboard.
Tension is important when thinking about strings for a nylon-stringed 3/4 guitar because the reduced size creates a different tone and feel. Given a 3/4 guitar is shorter in scale (distance between the guitar bridge and nut) it will take less tension to achieve the same note than it would on a regular guitar.
As a result, medium tension strings on a 3/4 guitar can sometimes sound and play more like light tension strings on a 3/4 guitar because of the shorter scale. So, to get the equivalent tone and tension on a smaller guitar you might need to use higher tension strings.
As the name suggests, string gauge, or thickness refers to the thickness of the strings. String sets are usually described with the thickness of their lightest and heaviest string. For example, a string set described as 10-52 means that the high E string is 10mm thick, and the low E string is 52mm thick. You often refer to a set of strings by the high E thickness. So a set of 10-52’s would be referred to as 10’s.
Light gauge strings are more flexible, so often preferred by people playing lead guitar, but they aren’t quite as loud as thicker gauge strings.
Though aspects like gauge and material will be consistent across different brands, many players find that the medium tensions on one brand are different to the medium tension of another brand. So it may take some trial and error to get the desired feel for the 3/4 guitar strings but it is worth the hassle to find a set you are comfortable with, then just buys those.
Overall, when buying strings for your 3/4 guitar it is the tension and gauge that you need to worry about, not the size of the guitar. You might need to experiment to find the tension that you prefer, keeping in mind that the impact of the tension will differ based on guitar size.
Though you can buy guitar strings for 3/4 specifically, these are largely just a marketing ploy, and they are standard strings, perhaps just trimmed slightly shorter.