Unless you're reminding someone that something specific exists, "there is" and "var" are used to talk about the existence of something which the listener is not aware of. It is inherantly indefinite.
(1) There is a spider on the wall.
(2) A spider is on the wall.
(3) The spider is on the wall.
(1) and (2 )are both talking about new or non-specific spider. The speaker doesn't think the listener will know which spider, and it doesn't matter which spider.. (1) is more natural than (2). In sentence (3), the spider is a specific spider. The speaker assumes the listener will know which one.
In Turkish, these are ... I think ...
(1) Duvarda (bir) örümcek var.
(2) (Bir) örümcek duvarda.
(3) Örümcek duvarda.
If it were "The spider is on the wall" it would be "Örümcek duvarda". If you really want to emphasise that it is A spider, you can make it "Duvarda bir örümcek var". As I understand it, the first word can always be considered definite as long as it's in the nominative case. If the word is the object of a verb, then it's a little more nuanced. If the object has bir, it's always indefinite. If it has the accusative it's always definite. If it has bu/şu/o it's always definite. Possessives seem to generally be definite as well, but there might be exceptions to that. Unless you use bir, locative, dative, ablative, and instrumental nouns seem to all be definite. The really confusing one is plural objects in the nominative case (like gazeteler in "Ben gazeteler okurum"). Hopefully that helps and is correct.