What is the different between tint, tint and shades and hue shift?

Good question! Here's how I understand these terms:

Hue is basically the simplest answer to "What color is that?". "Red" or "green" or "orange" ... etc.

Now before getting to the others, I want to introduce another term, saturation. This is "How strong is the color?". If your color is very pale you would say it has low saturation. Totally pure color is high (total) saturation.

Now Tint and Shade are both cases where saturation is reduced. When the reduction is made by making the color lighter, it's a tint, and when you make it darker, it's a shade. And if you reduce the saturation without making it lighter or darker, it's a tone.

Finally hue shift is exchanging one color for another, or when applied to a multicolor image, exchanging a whole set of colors for a different set. The "amount of shift" would determine which colors replace the others. For example, a slight hue shift might cause red to become orange and yellow to become green. A stronger hue shift might make red into yellow, and yellow into blue.

Are you familiar with the common color picker tool? There's a slider that adjusts the hue on the right, and for any hue there is a box where you pick a point that determines the saturation and "brighness". The edges of the box are the best examples of the terms you mentioned. The top edge is all tints, that vary from pure color on the right to white on the left. The right edge is shades, going from pure color at the top to black at the bottom. The left edge has no saturation (no color), and varies from white to grey to black. And the bottom edge is just black.

Inside the box, you have the whole variety of tints, tones, and shades, and they flow smoothly from one to another. It's probably not possible to categorize every point inside the box as just one of those terms.

Anyway, did this help? I got more wordy than I intended!