There are many types of herpes viruses and, yes, you can contract more than one type. For example, you can contract, both, HSV-1 and HSV-2. One does not make you immune to the other.
Shingles, however, cannot be 'caught'. It is not a virus that can be transmitted sexually. However, you can get Chicken Pox from being exposed to the shingles virus if you have not had Chicken Pox or Chicken Pox vaccination.
Types of Herpes Viruses
Herpes Virus - 1/Oral Herpes (cold sores or infected mouth region). HSV-1 is usually acquired by an upper respiratory tract infection as a child. It is possible for HSV-1 to cause genital herpes.
Herpes Virus - 2/Genital Herpes (genital or rectal region) can also be the cause of cold cores (HSV-1) and vice versa. Genital herpes can be caused by cold sores (HSV-1). In fact, genital herpes caused by HSV-1 (cold sores) is becoming more common place as blisters do not have to be present. HSV-1 is contagious during viral shedding. However, genital herpes caused by HSV-2 is more likely to cause recurrence later.
Herpes Virus - 3/Varicella-Zoster Virus (the cause of Chicken Pox and Shingles)
Herpes Equine Virus 3and Cyprinid Herpes Virus3 are unrelated to humans. They are related to horses and fish, particularly Koi (carp).