The concept of multiresolution has roots on the observation that in data (eg images), objects and features can be observed and processed at different resolutions. One of the crudest version is to build a pyramid with the original image, and other sub-sampled versions, keeping 1 out of 4, 1 out of 16... pixels.
This yields a crude multiresolution pyramid, which is not a wavelet per se.
Wavelets, in a strict sense, naturally yield a certain type of multiresolution, but satisfy other constraints (esp. invertibility), so they are only a quite useful way of doing multiresolution.
There are many fast ways to compute CWT, that differ from DWT, see for instance