그림으로 비교하면 이런 느낌이에요.

schedule() - 지정된 시간을 기다린 후 처리

import java.util.concurrent.Executors;
import java.util.concurrent.ScheduledExecutorService;
import java.util.concurrent.TimeUnit;

public class Main {

    public static void main(String[] args) throws Exception {
        ScheduledExecutorService service = Executors.newSingleThreadScheduledExecutor();

        service.schedule(() -> {
            System.out.println("end!!");
            service.shutdown();
            System.exit(0);
        }, 1, TimeUnit.SECONDS);

        int count = 0;
        while (true) {
            Thread.sleep(100);
            System.out.println((++count) * 100 + " ms");
        }
    }
}

100 ms
200 ms
300 ms
400 ms
500 ms
600 ms
700 ms
800 ms
900 ms
1000 ms
end!!

scheduleAtFixedRate() - 일정 시간마다 처리

import java.util.concurrent.Executors;
import java.util.concurrent.ScheduledExecutorService;
import java.util.concurrent.TimeUnit;
import java.util.concurrent.atomic.AtomicInteger;

public class Main {
    public static void main(String... args) throws Exception {
        ScheduledExecutorService service = Executors.newSingleThreadScheduledExecutor();

        AtomicInteger number = new AtomicInteger(0);
        service.scheduleAtFixedRate(() -> {
            int n = number.getAndIncrement();
            System.out.println("begin(" + n + ")");
            sleep(Math.max(1, 3-n));
            System.out.println("end(" + n + ")");
        }, 2, 2, TimeUnit.SECONDS);

        int count = 0;
        while (true) {
            TimeUnit.SECONDS.sleep(1);
            System.out.println((++count) + " s");
        }
    }

    private static void sleep(long seconds) {
        try {
            TimeUnit.SECONDS.sleep(seconds);
        } catch (InterruptedException  e) {}
    }
}

1 s
begin(0)
2 s
3 s
4 s
end(0)
begin(1)　←直前の処理が終了するまで待機させられている
5 s
6 s
end(1)
begin(2)
7 s
end(2)
begin(3)
8 s
end(3)
9 s
begin(4)
10 s
end(4)
11 s
begin(5)
12 s
end(5)
13 s
begin(6)
14 s
end(6)
15 s

scheduleWithFixedDelay() - 중복 처리가 완료될 때까지 일정 시간 기다림

import java.util.concurrent.Executors;
import java.util.concurrent.ScheduledExecutorService;
import java.util.concurrent.TimeUnit;

public class Main {

    private static int n = 0;

    public static void main(String[] args) throws Exception {
        ScheduledExecutorService service = Executors.newSingleThreadScheduledExecutor();

        service.scheduleWithFixedDelay(() -> {
            System.out.println("begin(" + n + ")");
            sleep(1000);
            System.out.println("end(" + n + ")");
            n++;
        }, 2, 1, TimeUnit.SECONDS);

        int count = 0;
        while (true) {
            sleep(1000);
            System.out.println((++count) + " s");
        }
    }

    private static void sleep(long ms) {
        try {
            Thread.sleep(ms);
        } catch (InterruptedException e) {}
    }
}

1 s
2 s
begin(0)
3 s
end(0)
4 s
begin(1)
5 s
end(1)
6 s
begin(2)
7 s
end(2)
8 s
begin(3)
9 s
end(3)
10 s

참고 자료