It depends on what you're specifically trying to say.
Linguistics
If you're trying to specifically contrast 「です」・「ます」 vs 「だ」・「る」, then you have a few options:
Use 「敬体」 and 「常体」.
(Note that they refer to the style (文体), not specific words like, say, 「丁寧語」 does; that is, 敬体≒丁寧語を用いた文体. If you are being anal about it.)
However, if you use these, no one will understand you except linguists or very well-read people, which should make sense, given that it's not normally useful to contrast this specific aspect of the language and the words are not particularly intuitive.
Use 「丁寧体」 and 「普通体」.
They are an, in my opinion, slightly more intuitive pair (which also refer to 文体s); however they are just as uncommon and also currently only in used by linguist-types AFAIK.
Use 「ですます体（or 調）」 and 「だ体」.
「ですます体」 is probably the most intuitive word that refers to 敬体・丁寧体, and is pretty common. 「だ体」 is also pretty intuitive, yet I feel like I rarely see it used compared to 「ですます体」.
Use 「丁寧語」 and ☹.
This is this most common of all the technical words; that said, it is still a technical word (and its technical meaning is slightly different from 「丁寧体」 as earlier described, but no one really cares about this to be honest :-). Understood by virtually anyone.
General Concepts
If you want something that people would understand, I'd personally recommend 「敬語」 and 「タメ口」 -- there's no one that won't understand that pair.
In common speech, they mean "respectful speech" and "casual speech" respectfully; basically they are as general as the English translations sound. So, 「タメ口」 doesn't just mean using 「だ」 but also contractions like 「ちゃう」 , endings like 「な」, 呼び捨て, etc, etc.
(Note, there are some people that will complain that 「敬語」 refers to specifically 謙譲語 and 尊敬語. But in common speech it really does just mean "respectful speech" as a general concept.)
Regarding the other things you listed:
- 「タメ語」 basically means the exact same thing as 「タメ口」, though I think it's slightly less common.
- 「くだけた表現」 doesn't really refer to a style but to an expression if we're trying to nitpick. However, 「くだけた口調」 seems like something worth discussing. I feel the difference here is that it's pointing out a different aspect of style than 「タメ口」 to me -- I feel like a sentence using です・ます could be described as くだけた口調, as long as, well, it's くだけた (relaxed/informal) -- like say 「そうですねー！僕も行きたいです＾＾」. I'd be more reluctant to call that タメ口 but would call it くだけた口調. (This is purely my opinion.)
- 「友達言葉」 seems pretty similar in meaning to 「タメ口」 to me -- I just think it's less common an expression.
- 「カジュアル」 is just an adjective -- if you said something like 「カジュアルな口調」 I think it'd basically mean the same as タメ口. Has the benefit of being pretty intuitive like 「くだけた」.
tl;dr
I'd use 「タメ口」 almost always. Possibly use 「だ体」 or 「常体」 if I'm talking linguistics.
