"A spider is small."
No, both are not acceptable. Because if you say only "küçük", without "-tür/dır etc."; you should say "The spider". Not "A spider" . When we talk about something generally as a specie, we use "-dır, -tür etc." .When we don't use this add( -dır, -tür) , it means we talk about something near of us signing.
The general rule says (Use d...!) ... but in the words ending with a voiceless consonant (k,t,ç,p,s,ş,f,h) you should use t instead. i,ı,u,ü ... used according to the 4WVH Rule. So you will get (dir,dır,dur,dür,tir,tır,tur,tür) Enjoy:küçüktür, ucuzdur, kısadır, sıcaktır, zayıftır, gençtir, gülüştür......
4 way vowel harmony (covered in the tips for accusative case). When adding a suffix to the end of the word, the vowel in the suffix with often follow a four way vowel harmony rule. If the last vowel of the word which you are adding the suffix to is: ü or ö, the vowel in the suffix is a ü. For example süt (milk) --> sütü (the milk) If the last vowel of the word which you are adding the suffix to is: u or , the vowel in the suffix is a u. For example Tavuk (chicken) --> tavuğu (the chicken - consonant harmony rules change the k to a ğ. If the last vowel of the word which you are adding the suffix to is: e or i, the vowel in the suffix is a i. For example peynir (cheese) --> peyniri (the cheese) If the last vowel of the word which you are adding the suffix to is: a or ı, the vowel in the suffix is a ı. For example, Çay (tea) ---> Çayı (the tea) The examples provided are for using the accusative case, although four vowel harmony like this, where the vowel in the suffix depends on the last vowel in the word, appears in many places in Turkish.
you can only use the accusative case on objects, not subjects.
You can say "Duo örümceği yer" (Duo eats the spider) but you cannot use "örümceği" as a subject...If you want to be specific you can say "o" (that, for close range), "şu" (that, for long range), or "bu" (this).
But since there is no article "the" in Turkish you can't definitely say "the spider eats cake" or something like that. However, it would be assumed if "örümceği pasta yer" was written, it would be "the spider" not "a spider" because if the author wanted to say "a spider" they would write "bir örümceği".
This is a long awkward answer but hopefully it makes sense.
They both are variations of the suffix “-DIr”
This is used in third person singular and plural to emphasise something or state facts.
The “D” in the suffix indicates consonant harmony. It can be a T or a D. If the word you are adding the suffix to ends in a voiced consonant or vowel, use D, unvoiced, use T (o sakindir = he is calm (a fact), o büyüktür = he is big (a fact)).
The I in the suffix is four way vowel harmony (the same system they use for the accusative case suffix). So the vowel changes depending on the last vowel in the word (ü,ö = ü... u,o = u.... e,i = i... a,ı = ı). Hopefully this helps - any questions just ask :)