Does Clojure make defn- distinct from declaring a function with ^:private?

The defn- macro simply abbreviates a "private" function declaration. Written out fully, it becomes:

(defn ^:private entry [inputs] ...)

This is really only a signal to users to avoid those functions. Bypassing this limited "private" protection for testing and similar tasks is straightforward. I avoid so-called "private" functions because of the inconvenience (occasionally I attach ^:no-doc metadata and choose names such as entry-impl to show a fn isn't within the public API and library consumers ought to disregard it).

For additional details, inspect how Clojure source code defines defn- (https://github.com/clojure/clojure/blob/38bafca9e76cd6625d8dce5fb6d16b87845c8b9d/src/clj/clojure/core.clj#L4925).

To address what was asked originally: they are equivalent.

user=> (defn- first_fn [value] value)
#'user/first_fn
user=> (defn ^:private second_fn [value] value)
#'user/second_fn
user=> (meta #'first_fn)
{:private true, :arglists ([value]), :line 1, :column 1, :file "NO_SOURCE_PATH", :name first_fn, :ns #object[clojure.lang.Namespace 0xcaf2cc4 "user"]}
user=> (meta #'second_fn)
{:private true, :arglists ([value]), :line 1, :column 1, :file "NO_SOURCE_PATH", :name second_fn, :ns #object[clojure.lang.Namespace 0xcaf2cc4 "user"]}
user=> (source defn-)
(defmacro defn-
  "same as defn, yielding non-public def"
  {:added "1.0"}
  [name & decls]
    (list* `defn (with-meta name (assoc (meta name) :private true)) decls))
nil
user=>

Examining the implementation of defn- shows it behaves exactly like defn after attaching :private true metadata to the name symbol.