.......All I want to know is, apart from the octave possibly being lower on a tenor than an alto - if I use the same fingering on both tenor and an alto - will the same note play on each? (albeit probably in a different octave?)
Not quite as easy as 'octaves' - tenor is in Bb (i.e. finger a 'sax' C and concert Bb comes out), and alto is in Eb (i.e. finger a 'sax' C and concert Eb comes out). 'Concert' in this case, for practical purposes, meaning 'same as piano, flute or guitar note'. As saxophone sizes increase (or decrease) the pitch alternates between Eb and Bb, so for saxes to be 'an octave' apart you have to skip a size.
The only way you could play two different saxes and have the 'same pitch' - but at an octave apart - is to either learn tenor + soprano (both in Bb), or alto + baritone (both in Eb). There are other combinations at extreme ends of the saxophone family, but I haven't mentioned those as they'd be far too difficult to start on (as are, in all honesty, soprano and baritone....)
So, if you learn play tunes by ear, then (e.g.) the finger patterns that you use for a tune on alto will come out at a different pitch on a tenor. Not a problem if you play alone, but with other instruments you'll have some funny harmonies.... If you do go for alto + tenor, you'll effectively have to learn each tune in a different key for each sax, if you play both in company.
As others have recommended, probably better to initially learn on only one sax, apart from pitch differences, you can develop an embouchure for just one sax much easier ! Also, playing by ear, if you have an ear that recognises pitch, and is able to associate the pitch with a certain sax fingering ( a useful skill), tenor and alto will have different fingerings for every (concert) note - another complication you probably don't initially need.
Hope that long-winded explanation helped. Unless you really want to play tenor from day one, initially learn alto - to take on two saxes 'at once' isn't like playing two different keyboards (and that wasn't meant to sound as patronising as it came out...).
P.S. and I didn't once mention "that's why I play C-Tenor and C-Soprano", don't go there if you're just starting out....