Memorial service is often used to describe a secular or non-religious funeral

Funeral

A funeral is a ceremony for celebrating, sanctifying, or remembering the life of a person who has died. Funerary customs comprise the complex of beliefs and practices used by a culture to remember the dead, from interment itself, to various monuments, prayers, and rituals undertaken in their honor...

. A funeral is a religious service that is held with or without the body of the deceased present. A memorial service is usually a secular service with or without the body present.

Alternatively, it is used to describe a less formal practice than a traditional funeral, and include such things as annual remembrance ceremonies, eulogies, music and fellowship. See Funeral#Memorial services

In the Orthodox church, a memorial service is a liturgy

Liturgy

Liturgy is either the customary public worship done by a specific religious group, according to its particular traditions or a more precise term that distinguishes between those religious groups who believe their ritual requires the "people" to do the "work" of responding to the priest, and those...

 performed in memory of the deceased, three, nine, forty days, one year and three years since the day of the funeral, see Memorial service (Orthodox)

Memorial service (Orthodox)

A memorial service is a liturgical observance in honor of the departed which is served in the Eastern Orthodox and Greek-Catholic Churches.-The service:In the Eastern Church, the various prayers for the departed have as their purpose: to pray for the repose...

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Some use the term "Memorial Service" for a service with no remains present and use the term "Funeral" when the remains of the deceased (Casket for body or Urn for ashes) are present.