A kernel is a more general concept, but an impulse response is a special case of a kernel. The term kernel is used to describe an integral transform:
$$(Tx)(t)=\int_{t_1}^{t_2}x(\tau)K(\tau,t)d\tau\tag{1}$$
The function $K(\tau,t)$ is called the kernel of the integral transform.
If you compare $(1)$ to the convolution
$$y(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)d\tau\tag{2}$$
then you see that the kernel of the convolution $(2)$ is given by
$$K(\tau,t)=h(t-\tau)\tag{3}$$
Note that in signal processing we regularly use integral transforms, each one with a different kernel. The most well-known examples are the Fourier transform, the Laplace transform, and the Hilbert transform (which is just a convolution).
It is also common to use (convolution) kernel to denote the impulse response of a discrete-time system.