The 1955 manual for the IBM 704 on page 7 talks about data representation in the computer.
When a word is interpreted as numerical data, the
zero position acts as the sign of the word. (…) When
a logical operation is performed on a word, the
word is interpreted as a 32-bit signless number.
As an algebraic (signed) binary number, a word can
In addition, there is a section, around page 19 on 'logical operations' in general, which include for example the obvious case of AND and OR, and the less-obvious (to me) CAL, clear and add logical word.
I conclude that focusing on the shift instructions is somewhat misplaced. The distinction is about the datatype and how the programmer intends to use it. Once you have that focus, then naming the shift instruction naturally follows.
Curiously, though, the 704 has a Logical Left shift but no Logical Right shift. Logical Left is distinguished from Long Left Shift by whether the sign bit of the MQ is involved (it is for Logical Left, it is not for Long Left).
Footnote: the 709 instruction set seems somewhat strange to me. In a 36-bit machine the accumulator has 38 bits: 35 "operand bits", a sign bit S, and the so-called P and Q bits.
The strangeness is in part due to the 709 being a sign-and-magnitude machine. "Arithmetic" operands are loaded into S and 1-35 as you might expect; P and Q are cleared. Thus a signed 36-bit operand is lengthened into 38 bits signed. Arithmetic operations may overflow into P and Q, but not further into S.
"Logical" operands are loaded into P and 1-35; Q and S are cleared. An unsigned operand is lengthened into 38 bits unsigned.
For shifts, the sign bit is not involved. Single-length shifts in the AC involve P, Q, and 1-35. There's no arithmetic/logical distinction. The only difference is double-length shifts involving the MQ. "Long left shift" does not involve the MQ's S bit; bits leaving MQ 1 end up in AC 35. "Logical left shift" include MQ S. MQ 1 goes to MQ S, and MQ S goes to AC 35.