A comparison does real work in an essay: it lets a claim you have established about one case carry over to another, which is cheaper than arguing both. That is also why it is checkable. “Similarly, private schools face the same pressure” claims the pressure is genuinely the same, and a reader who knows one obvious difference now has a reason to doubt the paragraph rather than the sentence.
The family divides by how strong the likeness is. “Similarly” and “likewise” claim close parallel. “In the same way” claims the mechanism is shared, which is stronger. “Just as … so too” is the most formal and the most emphatic, and it needs both halves — the construction is incomplete without its second clause, which is where it usually breaks.
The commonest error is not grammatical. It is using a comparison connector to introduce something that is merely also true: “Similarly, the government should invest in schools” after a paragraph about hospitals claims a parallel that has not been shown. The word promises the reader a likeness, and the sentence has to deliver one.
“Similarly” asserts the two cases behave alike. A reader who knows one difference will use it against you.
“Likewise” = close parallel. “In the same way” = shared mechanism, which is a stronger claim.
“Just as X, so too Y.” The construction needs its second clause, and dropping it leaves a fragment.
A second true statement is addition. Comparison needs the two cases to be alike in the relevant respect.
