Symmetric Simple Random Walk - Definition Clarification

Question

I'm finding conflicting answers everywhere, including in my own notes.

In the phrase "symmetric simple random walk", which part, "symmetric" or "simple" refers to having a probability of $0.5$ to go up/down, and which part refers to going up/down the same amount (i.e. $1$ unit)?

Answer 1

Simple means the possible transitions are only immediate left/right. Symmetric means the two transition probabilities are equal.