getDiffTimeBetweenCurrentDate.js

export function getDiffTimeBetweenCurrentDate (dateString = '', now = new Date()) {
  const dayInMilliseconds = 86400000
  if ([null, undefined, false, true].includes(dateString)) {
    return dateString
  }
  const date = new Date(dateString)
  const isInvalidDate = isNaN(date.getTime())

  if (isInvalidDate) {
    return dateString
  }

  const month = date.getMonth()
  const day = date.getDate()
  const hour = date.getHours()
  const minutes = date.getMinutes()
  const seconds = date.getSeconds()

  const buildMessage = (label, value) => {
    if (value !== 1) {
      return `${value} ${label}s atrás`
    }

    return `${value} ${label} atrás`
  }
  const notZero = value => value !== 0

  if (month !== now.getMonth()) {
    const diff = Math.abs(now - date)
    const days = Math.ceil(diff / dayInMilliseconds)

    return buildMessage('dia', days)
  }

  if (day < now.getDate() && notZero(day)) { return buildMessage('dia', now.getDate() - day) }
  if (hour < now.getHours() && notZero(hour)) { return buildMessage('hora', now.getHours() - hour) }
  if (minutes < now.getMinutes() && notZero(minutes)) { return buildMessage('minuto', now.getMinutes() - minutes) }
  if (seconds < now.getSeconds() && notZero(seconds)) { return buildMessage('segundo', now.getSeconds() - seconds) }

  return buildMessage('segundo', 1)
}

timeDifference.js

function timeDifference(current, previous) {
  const milliSecondsPerMinute = 60 * 1000;
  const milliSecondsPerHour = milliSecondsPerMinute * 60;
  const milliSecondsPerDay = milliSecondsPerHour * 24;
  const milliSecondsPerMonth = milliSecondsPerDay * 30;
  const milliSecondsPerYear = milliSecondsPerDay * 365;

  const elapsed = current - previous;

  if (elapsed < milliSecondsPerMinute / 3) {
    return 'just now';
  }

  if (elapsed < milliSecondsPerMinute) {
    return 'less than 1 min ago';
  } else if (elapsed < milliSecondsPerHour) {
    return Math.round(elapsed / milliSecondsPerMinute) + ' min ago';
  } else if (elapsed < milliSecondsPerDay) {
    return Math.round(elapsed / milliSecondsPerHour) + ' h ago';
  } else if (elapsed < milliSecondsPerMonth) {
    return Math.round(elapsed / milliSecondsPerDay) + ' days ago';
  } else if (elapsed < milliSecondsPerYear) {
    return Math.round(elapsed / milliSecondsPerMonth) + ' months ago';
  } else {
    return Math.round(elapsed / milliSecondsPerYear) + ' years ago';
  }
}

export function timeDifferenceForDate(date) {
  const now = new Date().getTime();
  const updated = new Date(date).getTime();
  return timeDifference(now, updated);
}

Perfeito, aplicado a melhoria aqui também. Excelente @matheus-carvalho