Due to their different sizes, the fingerings for the notes on the tenor saxophone and the alto saxophone are not exactly the same. However, there are many similarities between the fingerings, and players who are familiar with one saxophone can usually learn to play the other with relative ease.
Here is a chart showing the fingerings for the notes on the tenor saxophone and the alto saxophone:
Note | Tenor Sax | Alto Sax
-------|--------|--------
C4 | LH: 1, 2, 3, 4 | LH: 1, 2, 3
D4 | LH: Add pinky | LH: Add pinky
E4 | RH: Thumb, 1, 2 | RH: Thumb, 1, 2
F#4 | RH: Thumb, 1 | RH: Thumb, 1
G4 | RH: Thumb | RH: Thumb
A4 | LH: Lift 2 | LH: Lift 3
Bb4 | LH: Lift 3 | LH: Lift 4
As you can see, the fingerings for the notes in the lower register are very similar on both instruments. The main differences occur in the upper register, where the tenor saxophone has a larger range.
Overall, the fingerings for the tenor saxophone and the alto saxophone are quite similar. Players who are familiar with one instrument can usually learn to play the other with relative ease.