How sensitive to change are elliptic curve formulae In layman's terms? Take for example a curve from a recent question such as #25519:-

$$y^2 = x^3 + 486662x^2 + x$$

It's considered "safe".  What are are the implications of amending it very slightly to:-

$$y^2 = x^3 + 486664x^2 + x$$

I'm trying to get a layman's feel for what this would mean.  For example, is it now entirely invalid and can't be used at all, very easy to break or just a little easier to break? Or does this tiny change suddenly allow specific attacks to come into play?
An elliptic curve equation is very sensitive to any change of its parameters.

That small change result in a complete different curve.
Its security could be good or bad, but you have to check it explicitly and cannot make predictions beforehand.

Specifically, your resulting curve will have a composite order whose largest factor is $833860344743147476600479140946265460420135480673538361531$ which implies your curve's security won't exceed $2^{94.5}$.
I said "won't exceed" because I haven't checked all the other security properties of the curve (twist security, transfers, etc), which could result in a security downgrade.