version using String (not recommended)

#define LED 2
const char* a = "abcd";

void setup() {
  Serial.begin(115200);
  pinMode(LED, OUTPUT);
}

void loop() {
  if (Serial.available()) {
    String s = Serial.readStringUntil('\n');
    s.trim();
    if (s == a) {
      digitalWrite(LED, HIGH);
    } else {
      digitalWrite(LED, LOW);
    }
  }
}

the version with C-string:

#define LED 2
const char* a = "abcd";
char buffer[32];

void setup() {
  Serial.begin(115200);
  pinMode(LED, OUTPUT);
}

void loop() {
  if (Serial.available()) {
    size_t l = Serial.readBytesUntil('\n', buffer, sizeof(buffer - 1));
    if (buffer[l - 1] == '\r') {
      l--;
    }
    buffer[l] = 0; // the terminating zero
    Serial.println(buffer);
    if (strcmp(buffer, a) == 0) {
      digitalWrite(LED, HIGH);
    } else {
      digitalWrite(LED, LOW);
    }
  }
}

version using String (not recommended, but it makes simpler to understand the following C-string version)

#define LED 2
const char* a = "abcd";

void setup() {
  Serial.begin(115200);
  pinMode(LED, OUTPUT);
}

void loop() {
  if (Serial.available()) {
    String s = Serial.readStringUntil('\n');
    s.trim();
    if (s == a) {
      digitalWrite(LED, HIGH);
    } else {
      digitalWrite(LED, LOW);
    }
  }
}

the version with C-string:

#define LED 2
const char* a = "abcd";
char buffer[32];

void setup() {
  Serial.begin(115200);
  pinMode(LED, OUTPUT);
}

void loop() {
  if (Serial.available()) {
    size_t l = Serial.readBytesUntil('\n', buffer, sizeof(buffer - 1));
    if (buffer[l - 1] == '\r') {
      l--;
    }
    buffer[l] = 0; // the terminating zero
    Serial.println(buffer);
    if (strcmp(buffer, a) == 0) {
      digitalWrite(LED, HIGH);
    } else {
      digitalWrite(LED, LOW);
    }
  }
}