Also, same-day appointment and walk-in appointment

The Convenience of Walk-In Dental Appointments
Walk-in dental appointments help people get care without an appointment or with a same-day appointment. Clinics that take walk-ins may focus mainly on preventative care. It is easier to take walk-ins when you do not have to make time for more extensive procedures. A walk-in appointment can help you avoid missing work or planning too far ahead. If your schedule is always packed, you can sneak in a dentist appointment on a day that is less busy, even if you cannot plan for a day off.

https://www.westoremdental.com/the-convenience-of-a-walk-in-...

Urgent problems that threaten the health of your teeth or leave you in pain should not be ignored. You can expect to be seen by your emergency dentist quickly and without an appointment though it is recommended that you call your dentist’s office if possible before you arrive.

https://thesmileshoptahoe.com/dental-emergencies/

Whether you’re just overdue for a checkup and have some extra time, or you’re suffering from a DENTAL EMERGENCY and need treatment fast, Precision Dental is here to help. We always have same-day appointment slots available for our patients, so we can provide you with the treatment you need, when you need it.

https://www.precisiondentalbowlinggreen.com/post/are-you-loo...

This is how I understand it.

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Note added at 17 mins (2019-10-16 18:35:29 GMT)
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Son patologías buco-faciales, de aparición súbita, de origen múltiple, que se manifiestan principalmente por dolor agudo y que provocan una demanda espontánea de atención.
Urgencias dentales más comunes:

http://www.clinicamovident.cl/index.php/extensions

Este programa se encuentra a cargo del Sr. Germán Contreras, Cirujano- dentista, teniendo clínica dental en el CESFAM y en la Posta de Mocopulli, equipo dental portátil que atiende la población de la costa y la clínica móvil de JUNAEB que atiende en la escuela básica.
Este programa atiende demanda espontanea de la población en general , urgencias odontológicas , adolescentes , adultos mayores y funcionarios y atención preferencial a niños de 6 y 12 años, gestantes, y adultos de 60 años, se debe mencionar que el ingreso a los 6 años y las embarazadas corresponde a patologías AUGE.

http://www.corpodalca.cl/programa-de-salud-odontologia/

Em inglês: Humanized reception of patients without an appointment
Em espanhol: Acogida a la demanda espontánea

https://www.passeidireto.com/arquivo/20651095/acolhimento-a-...