Would is the past tense of the auxiliary verb will, which has a primary use as a marker of future time. It may seem odd that the word has a past form, but it comes to bear in what is called past futurate, which is contemplation of future action from the past. The verb form thus arises from the transposition of tense required for a report of direct discourse (i.e., a direct quote). Thus if I say she told me, "I will be sixteen in March," then I can later report that quote as
[1a] She told me that she would be sixteen in March.
Also consider following example that I borrow from a kind commenter:
[2a] She didn't know it when they met, but years later, she would be his wife.
They're married now, but they met in the past, and from that temporal vantage point, their marriage was in the future.
However, would has many modal meanings in English, i.e., meaning beyond an expression of past time. (The OED devotes several pages to the definition of will/would.) One of these indicates determination or intention:
[1b] She's thirty now, but she would be sixteen if she could.
[2b] She believed that if she only got his attention, she would be his wife.
Notice the difference from "... could be his wife," which expresses mere possibility. The would expresses her desire and intention to marry him. Compare this to the title of Rudyard Kipling's short story "The Man Who Would Be King."
Would can also express certainty upon consideration of evidence. For example, to answer the question, "How old is Alice?"
[1c] Let's see. She was born the year I graduated from high school, so she would be sixteen.
In answer to the question, "Is Jack's wife at the party?"
[2c] Did you see a tall, elegant woman in a long, black cocktail dress and red high heels? That would be his wife.
So in the OP's examples, how can we tell which sense is intended? We can't without more context, as I've tried to supply in my examples.