What's the difference between astronomical telescope, equatorial telescope and theodolite?

Theodolite uses horizontal-elevation coordinate system, and equatorial instrument uses right ascension-declination coordinate system. The latter can counteract the rotation of the earth, while the former will produce field rotation when taking pictures. Automatic star finding and electric tracking depend on the specific model. Generally, the stability of equatorial telescope is better than theodolite, but it is heavier. In a word, theodolite is suitable for visual inspection and going out, and equatorial instrument is suitable for photography.