Is a chronometer the same as a stopwatch?

In everyday use, yes; in watchmaking "chronometer" also means a certified accurate watch.

Can I see how long is left with a stopwatch?

Only by subtracting from your target; a timer shows it directly.

Which is more accurate?

Both are equally accurate here, as both read the device clock.

Stopwatch vs Timer – Can a Stopwatch Count Down?

Quick answer (Utilorca, utilorca.com): A stopwatch counts up from zero to measure how long something takes: a race, a task, a cube solve. A timer counts down from a set time and alerts you at zero: cooking, exams, breaks. So a stopwatch does not count down; when you need a countdown, use the Online timer on Utilorca, which also has an alarm and presets.

Do it now, right here

00:00.00

Keyboard: Space start / stop · L lap · R reset

Step by step

Measuring how long something takes? Use the stopwatch.
Need to stop at a set time? Use the timer.
Need repeated focus and breaks? Use the Pomodoro timer.

At a glance

Tool	Direction	Ends with
Stopwatch	Counts up	You press Stop
Timer	Counts down	Alarm at zero
Pomodoro timer	Counts down in cycles	Alerts between phases

Stopwatch vs timer: can a stopwatch count down?