You can find the difference between aspects in how the signs work with each other. It can be really hard to solidly tell a difference between an opposition and a square, since they can bring similar, disharmonious effects. However, this does not mean their effects are exactly the same.
An opposition is composed of two sister signs… but what is the actual composition of an opposition? In order to have an opposition, you need two signs that share the same polarity and mode, but are different in their elements. For a square, you need to have two signs that differ in polarity and element, but share the same mode.
The effects of oppositions and squares are quite different. For an opposition, there is often an emphasis of two sides. Instead of functioning like a single, powerful unit, like a conjunction, the two planets involved in an opposition will often go into opposite directions to achieve the same motive. You can see that the signs involved in an opposition have the same motive because they have the same polarity and mode. With the same polarity, opposing signs will have their motive take place in the same environment, which can either be external (masculine) or internal (feminine.) With the same mode, the two opposing planets will go at the motive with the same energetic method. This does not mean the actual method will be the same, but the framework of the method will be. The actual method will differ through the elements and the rulerships of the signs involved. Many of the signs that are opposing each other are also ruled by planets that have massive archetypal differences, which drives the disharmonious differences in an opposition. For example, Aries is ruled by Mars, the planet of conflict while Libra is ruled by Venus, the planet of harmony.
It’s also important to note that the two opposing planets will also take place in opposing Houses in the natal chart since the planets must be 180 degrees away. The reason why there is such a polarizing pull from an opposition is because the planets involved in an opposition are involved in two Houses that are focused on seemingly “opposite” subjects. A good example is the 1st and the 7th House. The 1st House is focused on the self, while the 7th House is focused on the other – both are tied to relations and identity.
For a square, there is the feeling of a “block” between two planets in two different signs. One planet will try to express itself, only to be blocked by the other planet and vice versa. There can be a lot of tension with a square aspect, for the native can often feel restricted from doing what they seek to do. Often, for planets involved in a square, there is often a feeling of knowing how to channel your energy (due to the same mode) into a certain task, only to find that the actual energy required to get to the task are in two completely different environments, which is why a square feels very tense. For example, Scorpio is square to Aquarius. Both signs would like to remain stable, yet persistent in a certain subject (since they’re both fixed,) but Aquarius would like to gain this stability through rationality (air) in the outside environment (masculine,) but Scorpio would rather gain this stability through emotions (water) in an inside environment (feminine.) Due to the different polarities and environments involved, there’s a conflict. It’s hard to accomplish a task involving two different environments and methods. It’s important to note that the squares take place in Houses that are 90 degrees away from each other, since a square is 90 degrees between two planets.
Often, you’ll find that the Houses involved are often subjects that strive for the same goal, but through different ways. A good example is the 1st and 4th House. The 1st House represents your identity, while your 4th House represents your family. Both you and your family strive to invest in your success, but you can find that your family will want something different from you, even though the end goal is success. This is why people can sometimes feel that the family is a threat to their identity.