Switching from sax to sax is relatively easy, the notes you read correspond to the same fingerings. Clarinet to sax takes a bit more concentration as the sax goes up an octave at a time with the register key but the clarinet is an octave and a 5th.

Its really not that hard with a bit of practice, and Id say clarinet to sax is easier than sax to clarinet at least.

The embouchure for sax and clarinet is a bit different though, dont make the mistake of thinking a sax is a metal clarinet or vice versa, clarinet embouchoure is a lot tighter.

 

My 9th grader is going through that right now (she's a clarinet/bass clarinet player since 5th grade and wants to play in one of the jazz bands). She's spent the last two months learning tenor sax and she's found the different fingering and embrochure to be the most difficult - not unexpected. After two months she figures she's roughly one method book behind where she is on clarinet, plus she's having to learn some rythmic elements she hasn't encountered before (e.g. swing). Her brother has been helping her with jazz rythms and such.

 

If you can play bass clarinet the transition should be quite easy. The only difference in embouchure will be that you will need to loosen up and form your lips like a drawstring pouch.
Fingerings, if you remember from alto, are almost identical to the second register on clarinet. Middle staff B and C will probably give you the most trouble remembering. It's not hard to accidentially go into 'clarinet mode'.
Unless you'll be soloing I really wouldn't worry too much about 'the notes in each key'. Just play what's in front of you for a while until your ears get accustomed to the new sound.

 

Tenor and Alto sax have the same fingerings, however Tenor is in B flat - the same as Clarinet, so you can use a lot of your old clarient music for it. Which can help if you want to give sax a try without having to invest in lots of new books and music.

 

I've never met a clarinet player who had much of a problem transitioning to the saxophone. There were quite a few clarinet players in my junior high and high school bands who were recruited to play sax in the jazz band, and every one of them made the transition very easily. When I started in beginning band it was a requirement that anyone who eventually wanted to play saxophone had to start on clarinet. That requirement was waived for me because my father and the band director happened to be friends from childhood. It took me around 10 years to understand why the clarinet requirement had been there, and I've wished ever since that I had started on clarinet. Generally, transitioning from clarinet to saxophone is easy. Since you've already played the sax for a year (even though it was quite a while ago), the transition will be that much easier for you. Don't sweat it. Just have a fingering chart handy in case you need to refresh your memory, and you'll be fitting in with the rest of the saxophone section in a matter of weeks. Whether it's alto, tenor, or baritone doesn't really matter. You'll pick it up pretty quickly, and I'm sure your band director (if they deserve to call themselves a band director) will be able to help you work out the embouchure differences.

 

One thing you might try — I'm not as fanatical about long tones as some are around here but I think they can be very useful for developing the proper sax embouchure and contrasting it with that of the clarinet. Play a note in the upper register, say a "B". Hold it for 10, 12, or 20 seconds. Then do it again but drop your jaw to lower the pitch. Try to sound a "Bb" while fingering a "B". Work on that for a while. Then see if you can get an "A" while fingering a "B". See if you can get even lower, all the while fingering a "B". This will give you some idea of the tonal flexibility of the horn, one of the key differences between the two closely-related instruments.