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Church Slavonic texts often appear in a particular old style of script. The lettering is related to Glagolitic and Blackletter (Gothic) in its parallel-line construction and dense packing. It does not seem to share much of the Uncial heritage of modern Cyrillic writing. A very jaunty skew occurs on the "O" in order to form it from two long lines.
What is the name of this old type of lettering?
If i'm not mistaken it must be титульный шрифт (from the obsolete титул - title, since it was used to inscribe book/chapter titles), or титульная вязь, which i'm not sure is an accurate name because it only becomes вязь when the letters are combined into ligatures or in other decorative ways. And i suppose it's based on устав.
you may be also interested in кириллическая вязь 
This group of fonts may not have a specific name, other than Church-Slavonic fonts. Such fonts usually support other features of Church-Slavonic language, such as extra letters, diacritics, titles and superscripts.
Often enough it's not only a different font, but also a different language. In the icon that you provided in the question, the inscription at the top says: "РЕЧЕ ГДЬ СВОИМЪ УЧЕИКОМ". The spelled out form (Гдь -> Господь, учеиком -> учеником) is Рече Господь своимъ учеником / Says God to his disciples. As you can see from the grammar, it's not Russian language.
Here is another example of text in Church Slavonic. It has an upper case narrow "O" in the title line, lower case narrow "o" in the second line, broad capital "O" in the third line, and lower case "omega" in the third line. Church-Slavonic has multiple glyphs for sound "O".
Here are some more fonts that can be used for Church-Slavonic publications.
АНАЛИТИЧЕСКОЕ ОБОЗРЕНИЕ formatted in Church Slavonic font is probably meant to create "faux antique" effect.
