Can I fit 27.5 or 29 tires on 700c rims?

700c is the same rim bead-seat diameter ETRTO-622 and the same as road 28" and the same as MTB 29" (29er).

So yes, you can fit 29" tyres on a 700c rim (of course, subject to the tyre and rim width compatibility What is the maximum or minimum tire width I can fit on my bicycle).

Your confusion may stem from the fact that while it is common in the MTB world to call this wheel size 29" (the approximate outer diameter of the tyre), in road and hybrid bikes it is commonly denoted as 700c or 622 (the rim size) and the outer diameter of the tyre is often more like 28" just because the road, gravel or hybrid tyres are smaller.

Vladimir is correct that 700c and 29er rims have the same bead-seat diameter. However, it's important to keep in mind that rims have a limited range of tire widths that they can handle, and 2" tires might exceed the maximum width of your rims. The rim manufacturer will probably have a tire-size guide, something like this.

Also, even assuming the rims can handle the tires, you'll want to make sure that the tires will fit your frame and fork. Chainstay clearance and fork-crown clearance in particular can be a problem. I've even discovered that the front derailleur can interfere with tires that are too wide.