One distinguishing element is that science is observable, verifiable, and can be duplicated while religion cannot be observed or proven. It is simply a set of beliefs which cannot be verified.
Science is not observation. Religion is observable. For example, it is easy to observe a pagan dance or a Christian worship service.
Science does not verify or prove anything. Religions try to 'verify' and prove themselves as the Truth.
Science is a set of falsifiable theories.
Religion simply assumes a Truth.
I asked you to define religion, not science.
Here is mine:
The best way to define 'religion' is by describing a common characteristic that all of them have.
The core of any religion is some initial circular argument. The other name for this type of argument is an Argument of Faith. You simply assume the argument to be True.
ALL other arguments for that religion stem from that initial circular argument.
For example: In Christianity, the initial circular argument is that Christ exists and that He is who He says He is, namely, the Son of God.
EVERYTHING else about Christianity stems from that initial circular argument.
In Shinto, the spirits and demons occupying various objects are simply assumed to be there. EVERYTHING else about Shinto stems from that initial circular argument.
In the Church of No God, they simply assume that no god or gods exist. EVERYTHING else about the Church of No God stems from that initial circular argument.
Thus: The definition of a religion is any belief based on some initial circular argument that simply assumed to be True, and with other arguments extending from that.
Therefore, the following are religions:
Christianity.
Buddhism.
Shinto (including it's American and African forms).
Islam.
Judaism.
The Church of No God.
The Church of the Big Bang.
The Church of the Continuum.
The Church of Creation.
The Church of Abiogenesis.
The Church of the Ozone Hole.
The Church of Global Warming.
The Church of Covid.
The Church of Hate.
The Church of Karl Marx.
The Church of Green.
Hinduism.
Some of these have a god or gods, some do not.
You seem to think that science is a proof of some kind, or that a theory can be proven True. That is fundamentalism. It is not possible to prove any theory True.