axial resolution is what we just talked about: differentiating 2 objects that are in the same axis (one is closer to the probe and one is further) where frequency is very important
lateral resolution is a different resolution where 2 objects are side by side. When we talk about the focus of the ultrasound beam (which we will do later), we will discuss lateral resolution. Lateral resolution is not dependant on frequency.
temporal resolution is a third type and refers to moving objects. Temporal = time, so we are referring to the ability of the image to show moving images. This is where frame rate comes into play.