I’m far from an expert on native American customs but I think smudges uses dried herbs bound in a bundle or burned in a shell.
Afaik this is directed solely toward the Holy Trinity, serving as a cultural symbol of purification before God
powwows.com says:
“Smudging is a Native American ritual that links smoke with spirituality in remarkable ways. This is a common ceremonial ritual among indigenous people, held closely within these cultures to purify, spiritually cleanse, rid physical spaces of negative energy, and bless.”
AI Overview says:
“Incense is used in Catholic Mass to symbolize prayers rising to heaven and to sanctify the altar, Gospel, offerings, and people, a practice rooted in Scripture such as Exodus 30 and Psalm 141.
Core Reasons for Using Incense
Symbol of prayers rising to God
The rising smoke visually represents the faithful’s prayers ascending to heaven, echoing Psalm 141: “Let my prayer come like incense before you.”
Sanctification and purification
Incense signifies the holiness of the altar, Gospel book, offerings, priest, and congregation. It marks them as set apart for God.
Biblical foundation
God commanded incense use in worship (Exodus 30), and Revelation depicts heavenly worship surrounded by incense offered with the prayers of the saints.
Connection to heavenly worship
Incense creates an atmosphere reflecting the worship of angels and saints, linking the earthly liturgy to the heavenly one.
Engaging the senses
Catholic worship involves the whole person—body and soul. Incense engages smell and sight to deepen reverence and solemnity.”
Seems to be little difference; like many other things, it depends on intention and what is in the heart.
Prove it, Cronos.
The prayer in the four directions is a pagan prayer traditionally understood to be directed to the Creator but also calls upon “spirits” associated with the North, South, East and West.