700c tyres come in widths from below 20mm to above 45mm. You have to match your tyre width to your rim.
The inner tube must match the width of the tyre.
The 700c tube also fits 27"tyre and often has both sizes printed on the box and embossed onto the tube.
Inner tubes can be used with a range of 700c tyre widths, and this is printed on the box. Given a choice between a thinner and a fatter inner tube I prefer a thiner one for low weight.
My bike is fitted with 700c/32mm tyres and my inner tubes are suitable for 25-32mm tyres. I could fit one suitable for 32-45mm but it would have a lot of excess material.
Besides the width, you need a valve the correct type for the hole in your rim (thin presta or fat schraeder) and the correct length (short for square-section rim shapes, long for aerodynamic rims).
Given a choice between a thinner and a fatter inner tube I prefer a thiner one for low weight.
Tansc, the other numbers on the tube/box indicate the recommended suitable tire widths, usually shown with a slash between the narrower and wider ranges: ie, 700 x 20/25, 700 x 35/43. The range is possible because tubes can expand.
Some people chose the thicker tube on the theory that a thinner tube will be stretched even thinner in the tire and thus present a thinner material to be punctured. Sounds logical, but the difference is probably pretty meaningless: once you get that thorn or sliver of glass, the tube's going to go sooner or later. But I thought I'd note the other point of view, especially considering that the weight difference is, for most of us, also pretty inconsequential.