Suppression hearing but no Franks hearing?
When law enforcement uses a search warrant to obtain evidence and that evidence is used at trial, the defense will likely attempt to have that evidence suppressed if there is an issue with the search warrant. But there can be two separate and distinct "issues" with a search warrant.
First, the defense could argue that the search warrant affidavit does not contain the required probable cause to search or seize the items. Or that the search warrant is general and does not particularly describe what is being sought.
Second, the defense could argue that law enforcement gave false or misleading information in the affidavit.
The first situation calls for a suppression hearing and the second situation calls for a Franks hearing (438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978)).
A recent Fourth Circuit unpublished opinion briefly described this:
United States v. Minnick, No. 17-4184, 2020 WL 1027671, at *2 (4th Cir. Mar. 3, 2020)
Also see District Court of S.C. local rule 12.06 Hearings on Motions, which give the judge discretion of whether to have an actual hearing on a motion.