Is a medium taper the same thing as number 1 on the sides?
a short taper is tapered with a fine clipper blade to at least an inch above the ear and then with coarse clipper blades above that; lower edge at the nape is tapered to the skin. A medium taper might have the sideburns tapered in coarse clipper blade range on the sides. At the back, the taper is in the coarse clipper blade range no higher than the middle of the ears with the lower edge at the nape tapered to the skin with a fine clipper blade; the rest of the back/sides are cut shears/comb or clipper over comb.
Fine clipper blades are the zero blades: #0A, #0, #00, #000, #0000A, #0000, #00000, #000000, #0000000. Coarse clipper blades are #1, #1A, #1.5, #2 #3.5. Fade actually refers to a taper in the zero blade range; the taper lever on fade clippers adjusts between #000 and #00000 blade lengths. All fades are tapers; all tapers are not fades. A good barber can usually design a regular haircut or one of the short pomp(pompadour) styles-crew cut, ivy league(long crew cut), flat top crew cut- to fully suit most young guys.
Most girls are fine with whatever standard medium to short style a guy chooses to wear as long as the style fully suits and is kept clean and looking well groomed and the guy doesn't spend a lot of time on his hair. If a guy wants to go to a shorter style for the summer or one of his sporting activities, that is fine with most girls even when she prefers that he wear a somewhat longer style. Hair grows at an average rate of 1/8" per week. A photo is the best way to describe a style to a barber or stylist.