Learn Finnish: Ovatko nämä kaksi kuviota samanlaiset vai erilaiset? - Are these two patterns similar or different?

Normally, a subject starting with a number greater than one takes a singular verb in Finnish (e.g., kaksi kuviota on). However, because we added the plural word nämä (these) in front of the number, it forces the whole subject block to act as a plural, which makes the verb plural: ovatko nämä kaksi...

Why do the adjectives samanlaiset and erilaiset end in a plural "-t" instead of matching the partitive singular "kuviota"?

Because the subject is treated as plural (thanks to nämä), the predicative adjectives (the adjectives describing the subject after the verb "to be") must also be in the nominative plural form. They agree with the plural idea of "these", not just the word "pattern".

Could I use "tai" instead of "vai" for "or" in this sentence?

No. In Finnish, vai is used specifically in questions where you are offering mutually exclusive options (the patterns have to be either similar OR different; pick one). Tai is used in statements or open-ended questions.

How would I use "toinen ... toinen" to answer this by saying: "One is similar, the other is different"?

You would say: Toinen on samanlainen, toinen on erilainen. When you split the two patterns up using toinen ... toinen (one ... the other), you are talking about them individually. Therefore, the verb becomes singular (on) and the adjectives drop their plural -t.