The top of a slide-in stove lays on top of the countertop stone/material and covers it about 1-1/4 inches on each side and the back. There is no gap between stove top and countertop sides. A slide-in stove does not have "finished" metal sides. Cabinets on either side are required. A free-standing stove is just that...there will be a gap of some size between the countertop and the sides of the stove. A free-standing stove has finished metal sides and it can stand against a wall without any side cabinets.

Pretty nearly all slide-in ranges have a (usually metal) piece available to use as filler behind them, for situations like yours. A piece of the actual countertop material looks nicer, but if you don't plan to do counters, the manufacturers have thought of that.

Also remember that the free-standing range will have less cooktop surface due to the panel in the back taking up several inches of the cooktop. This can be a problem if you have a big dutch oven or something like that on the stove. Having said that, note that some slide-ins will have oven fans that are noisier and stay on longer. That's because the range's electronics are right on top of the oven and need to be cooled (vs. the freestanding where the electronics are in the panel in the back). Some say that with the general noise going on in their kitchens, they don't mind the fan noise. I myself chose a slide-in. I didn't want even an inch of space lost on my cooktop, and also I simply don't like the appearance of the free-standing ranges with the panels in the back.

Not quite sure I understand the problem. AFAIK, some brands of slide-ins (such as GE) are built to go against the back wall just like a freestanding stove while other brands (such as Electrolux) have bump outs in the back (for their ovens). The latter --- the ones with bumpouts in the rear --- require a countertop filler strip behind the stovetop. So, is the issue that your old Jenn Air had a countertop filler strip and you've only seen slide-ins that don't require them? Or is it the other way around? I'm also unclear about "doesn't overlap the counter?" Are you asking about overlapping in back or on the sides? Or are you talking about the base of the side overlap/projections being too high and leaving a gap to the countertop below it? Most stoves marketed as "slide-ins" do in fact extend over the side countertops. The trouble that has generated a lot of commentary here is that a lot of kitchen counters are 35 ½" high (or a little shorter) but the limits on the adjusting feet on a many ranges mean that you can't lower the range enough to touch the countertops which are less than 36" (or so) above floor level.. Apparently, the stove designers think we allnow ought to have countertops at least 36" above floor level. There are some stoves that you might think of as slide-ins --- ranges with minimal or no backsplash and all controls down front --- but these generally are marketed in other categories. GE's Cafe ranges are an example -- GE deliberately calls them freestanding ranges. Whirlpool is marketing similar stoves under its KitchenAid and JennAir brands. (The induction versions have not made it to market yet, but the radiant electric, gas and dual fuel versions have,) All "pro-style" ranges are this way, too, but, again, they usually are not marketed as "slide-ins".