At the time she has asked for both using the chen which the king has shown her. Once Haman is dead and Mordechai made the King's representative, she sees that only the first part of her request has been granted. She (and those close to her) are now safe. However, the king has not acted to cancel the evil that Haman has done.
The explicit statement in the second pasuk is not given in the first pasuk because it is implicit in Esther 7:3
may my life be given me in my petition and my people in my request
It was only when the king did not act on the implicit request that she had to ask explicitly.
Then the king extended the golden scepter to Esther, and Esther arose
and stood before the king.
shows that Esther had to approach the king again and
Esther 8:9 shows this as was over two months later.
And the king's scribes were summoned at that time, in the third
month-that is the month of Sivan-on the twenty-third day thereof, and
it was written according to all that Mordecai commanded, to the Jews
and to the satraps and the governors, and the princes of the provinces
from Hodu to Cush, a hundred and twenty-seven provinces, every
province according to its script and every nationality according to
its tongue, and to the Jews according to their script and according to
Esther had to approach the king a second time since she sees that the results of the first time only saved her and her immediate entourage. Noone would now dare attack those under the immediate eye of the king, but the decree making everyone else outside the palace fair game was still in effect. Thus she had to make the request more explicit and reiterate the argument.
She could not repeat the first argument as she is now safe.