Let's see it with an example,

R = k * G  mod N

Where k is the random number, G is the Gen point, and N is the order of the curve.

If I take  k randomly = 633cbe3ec02b9401c5effa144c5b4d22f87940259634858fc7e59b1c09937852

k* G = 02e9d4436e5e57ac598594faf9a04b8edc69a04096863ef4bd5a27dfcdc8c89fed (compressed)

k+1 * G = 0313e264d56097d32b38e23c6218b951ed02a684dccee5036388df1e6b94b5417a

The difference between them is enormous.  I don't know numbers that generate consecutive public keys with slight differences.

When you say slight difference, how small is it? Do you have a range?