I can say almost anything what I want in English by simply thinking it first in my regional language. That's easy but the trap is idioms. In every language idioms are so wonderful as they convince the matter with beautiful words in short. In a few words, you can describe many things.
We, in our regional language, have a wonderful idiom which literally translates to
Truth but not exactly the truth; a tricky truth [I wonder, whether this translation itself is an idiom!]
But it's not exactly what the idiom describes. Being diplomatic is quite close to this because you tell the truth in a way, in a smart way that does not look like an authentic statement, but still, is not a lie either!
Let me think of an example to make it clearer.
"[On phone] Dad, bring me those yummy chocolates from Denmark."
"Sure, but only if I travel by an airplane." [This is that idiom but the listener does not know about it yet].
"Yeah, no problem!" — The kid is pretty sure. (How else would her dad travel?)
After reaching home
"Dad, where are my chocolates?"
"Hey, I didn't bring them!"
"Why??? You said you'd bring them if you travel by airplane and you did travel, didn't you?"
"Yeah but I traveled by car as well! How do you think I reached home?"
The kid is sad. Now she knows that that sentence was actually [an idiom here].
"Hey, don't be sad… here are your chocolates, my darling!"
The kid's happy!
The most important thing to mention: This idiom is not restricted to be used to create a pun, but in some extreme cases can be fatal or catastrophically damaging.
The great epic (Mahabharata mentions this in the Day 15 of the Kurukshetra War):
After King Drupada and King Virata were slain by Drona, Bhima, and Dhristadyumna fought him on the fifteenth day. Because Drona was very powerful and inconquerable having the irresistible brahmadanda, Krishna hinted to Yudhisthira that Drona would give up his arms if his son Ashwathama was dead. Bhima proceeded to kill an elephant named Ashwathama, and loudly proclaimed that Ashwathama was dead. Drona approached Yudhisthira to seek the truth of his son's death. Yudhisthira proclaimed Ashwathama Hatahath, naro va Kunjaro va (-the idiom), implying Ashwathama had died but he was nor sure whether it was a Drona's son or an elephant, The latter part of his proclamation (Naro va Kunjaro va) were drowned out by sound of the conch blown by Krishna intentionally (a different version of the story is that Yudhisthira pronounced the last words so feebly that Drona could not hear the word elephant). Prior to this incident, the chariot of Yudhisthira, proclaimed as Dharma raja (King of righteousness), hovered a few inches off the ground. After the event, the chariot landed on the ground as he lied.
And solely due to [that idiom] this was the result:
Drona was disheartened, and laid down his weapons. He was then killed by Dhristadyumna to avenge his father's death and satisfy his vow.
Best Answer
Your first example, where the sentence is technically true but conveys a false meaning, would be considered sophistry in English. Informally, we might call these weasel words or, in some situations, use the recently coined word truthiness.
If you tell the truth about something, but hold something back, as in your second example, you could call that a half-truth. If you say, "I can't be drunk, I only had one beer," but you also drank a bottle of vodka, that would be a half-truth. This seems closer to your second example.
However, in my experience, most English speakers would be more likely to describe these situations in more general terms, as a trick, than to use a term specific to this sort of language.